1
|
Gao X, Xu Y. Markovian Approach for Exploring Competitive Diseases with Heterogeneity-Evidence from COVID-19 and Influenza in China. Bull Math Biol 2024; 86:71. [PMID: 38719993 DOI: 10.1007/s11538-024-01300-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2024] [Accepted: 04/19/2024] [Indexed: 05/23/2024]
Abstract
Due to the complex interactions between multiple infectious diseases, the spreading of diseases in human bodies can vary when people are exposed to multiple sources of infection at the same time. Typically, there is heterogeneity in individuals' responses to diseases, and the transmission routes of different diseases also vary. Therefore, this paper proposes an SIS disease spreading model with individual heterogeneity and transmission route heterogeneity under the simultaneous action of two competitive infectious diseases. We derive the theoretical epidemic spreading threshold using quenched mean-field theory and perform numerical analysis under the Markovian method. Numerical results confirm the reliability of the theoretical threshold and show the inhibitory effect of the proportion of fully competitive individuals on epidemic spreading. The results also show that the diversity of disease transmission routes promotes disease spreading, and this effect gradually weakens when the epidemic spreading rate is high enough. Finally, we find a negative correlation between the theoretical spreading threshold and the average degree of the network. We demonstrate the practical application of the model by comparing simulation outputs to temporal trends of two competitive infectious diseases, COVID-19 and seasonal influenza in China.
Collapse
Affiliation(s)
- Xingyu Gao
- School of Mathematics and Statistics, Changshu Institute of Technology, Changshu, 215500, China.
| | - Yuchao Xu
- GE HealthCare Technologies Inc, No. 1 Huatuo Road, Shanghai, 201210, China
| |
Collapse
|
2
|
Granger T, Michelitsch TM, Bestehorn M, Riascos AP, Collet BA. Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks. ENTROPY (BASEL, SWITZERLAND) 2024; 26:362. [PMID: 38785610 PMCID: PMC11120256 DOI: 10.3390/e26050362] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2024] [Revised: 04/21/2024] [Accepted: 04/23/2024] [Indexed: 05/25/2024]
Abstract
We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barabási-Albert (BA), Erdös-Rényi (ER), and Watts-Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers RM,R0 with and without mortality, respectively, and prove that RM1, the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others.
Collapse
Affiliation(s)
- Téo Granger
- Sorbonne Université, Institut Jean le Rond d’Alembert, CNRS UMR 7190, 4 Place Jussieu, 75252 Paris, Cedex 05, France (B.A.C.)
| | - Thomas M. Michelitsch
- Sorbonne Université, Institut Jean le Rond d’Alembert, CNRS UMR 7190, 4 Place Jussieu, 75252 Paris, Cedex 05, France (B.A.C.)
| | - Michael Bestehorn
- Institut für Physik, Brandenburgische Technische Universität Cottbus-Senftenberg, Erich-Weinert-Straße 1, 03046 Cottbus, Germany;
| | | | - Bernard A. Collet
- Sorbonne Université, Institut Jean le Rond d’Alembert, CNRS UMR 7190, 4 Place Jussieu, 75252 Paris, Cedex 05, France (B.A.C.)
| |
Collapse
|
3
|
Han Z, Wang Y, Gao S, Sun G, Wang H. Final epidemic size of a two-community SIR model with asymmetric coupling. J Math Biol 2024; 88:51. [PMID: 38551684 DOI: 10.1007/s00285-024-02073-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2023] [Revised: 02/11/2024] [Accepted: 02/29/2024] [Indexed: 04/02/2024]
Abstract
Communities are commonly not isolated but interact asymmetrically with each other, allowing the propagation of infectious diseases within the same community and between different communities. To reveal the impact of asymmetrical interactions and contact heterogeneity on disease transmission, we formulate a two-community SIR epidemic model, in which each community has its contact structure while communication between communities occurs through temporary commuters. We derive an explicit formula for the basic reproduction number R 0 , give an implicit equation for the final epidemic size z, and analyze the relationship between them. Unlike the typical positive correlation between R 0 and z in the classic SIR model, we find a negatively correlated relationship between counterparts of our model deviating from homogeneous populations. Moreover, we investigate the impact of asymmetric coupling mechanisms on R 0 . The results suggest that, in scenarios with restricted movement of susceptible individuals within a community, R 0 does not follow a simple monotonous relationship, indicating that an unbending decrease in the movement of susceptible individuals may increase R 0 . We further demonstrate that network contacts within communities have a greater effect on R 0 than casual contacts between communities. Finally, we develop an epidemic model without restriction on the movement of susceptible individuals, and the numerical simulations suggest that the increase in human flow between communities leads to a larger R 0 .
Collapse
Affiliation(s)
- Zhimin Han
- School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, Hubei, China
| | - Yi Wang
- School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, Hubei, China
| | - Shan Gao
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada
- Interdisciplinary Lab for Mathematical Ecology and Epidemiology, University of Alberta, Edmonton, AB, T6G 2G1, Canada
| | - Guiquan Sun
- School of Mathematics, North University of China, Taiyuan, 030051, Shanxi, China
| | - Hao Wang
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada.
- Interdisciplinary Lab for Mathematical Ecology and Epidemiology, University of Alberta, Edmonton, AB, T6G 2G1, Canada.
| |
Collapse
|
4
|
Kwon S, Park JM. General protocol for predicting outbreaks of infectious diseases in social networks. Sci Rep 2024; 14:5973. [PMID: 38472283 DOI: 10.1038/s41598-024-56340-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2023] [Accepted: 03/05/2024] [Indexed: 03/14/2024] Open
Abstract
Epidemic spreading on social networks with quenched connections is strongly influenced by dynamic correlations between connected nodes, posing theoretical challenges in predicting outbreaks of infectious diseases. The quenched connections introduce dynamic correlations, indicating that the infection of one node increases the likelihood of infection among its neighboring nodes. These dynamic correlations pose significant difficulties in developing comprehensive theories for threshold determination. Determining the precise epidemic threshold is pivotal for diseases control. In this study, we propose a general protocol for accurately determining epidemic thresholds by introducing a new set of fundamental conditions, where the number of connections between individuals of each type remains constant in the stationary state, and by devising a rescaling method for infection rates. Our general protocol is applicable to diverse epidemic models, regardless of the number of stages and transmission modes. To validate our protocol's effectiveness, we apply it to two widely recognized standard models, the susceptible-infected-recovered-susceptible model and the contact process model, both of which have eluded precise threshold determination using existing sophisticated theories. Our results offer essential tools to enhance disease control strategies and preparedness in an ever-evolving landscape of infectious diseases.
Collapse
Affiliation(s)
- Sungchul Kwon
- Department of Physics, The Catholic University of Korea, Bucheon, 14662, Korea
| | - Jeong-Man Park
- Department of Physics, The Catholic University of Korea, Bucheon, 14662, Korea.
| |
Collapse
|
5
|
Persoons R, Sensi M, Prasse B, Van Mieghem P. Transition from time-variant to static networks: Timescale separation in N-intertwined mean-field approximation of susceptible-infectious-susceptible epidemics. Phys Rev E 2024; 109:034308. [PMID: 38632755 DOI: 10.1103/physreve.109.034308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2023] [Accepted: 02/15/2024] [Indexed: 04/19/2024]
Abstract
We extend the N-intertwined mean-field approximation (NIMFA) for the susceptible-infectious-susceptible (SIS) epidemiological process to time-varying networks. Processes on time-varying networks are often analyzed under the assumption that the process and network evolution happen on different timescales. This approximation is called timescale separation. We investigate timescale separation between disease spreading and topology updates of the network. We introduce the transition times [under T]̲(r) and T[over ¯](r) as the boundaries between the intermediate regime and the annealed (fast changing network) and quenched (static network) regimes, respectively, for a fixed accuracy tolerance r. By analyzing the convergence of static NIMFA processes, we analytically derive upper and lower bounds for T[over ¯](r). Our results provide insights and bounds on the time of convergence to the steady state of the static NIMFA SIS process. We show that, under our assumptions, the upper-transition time T[over ¯](r) is almost entirely determined by the basic reproduction number R_{0} of the network. The value of the upper-transition time T[over ¯](r) around the epidemic threshold is large, which agrees with the current understanding that some real-world epidemics cannot be approximated with the aforementioned timescale separation.
Collapse
Affiliation(s)
- Robin Persoons
- Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands
| | - Mattia Sensi
- MathNeuro Team, Inria at Université Côte d'Azur, 2004 Rte des Lucioles, 06410 Biot, France
- Department of Mathematical Sciences "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
| | - Bastian Prasse
- European Centre for Disease Prevention and Control (ECDC), Gustav III's Boulevard 40, 169 73 Solna, Sweden
| | - Piet Van Mieghem
- Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands
| |
Collapse
|
6
|
Ullah MS, Kamrujjaman M, Kabir KMA. Understanding the relationship between stay-at-home measures and vaccine shortages: a conventional, heterogeneous, and fractional dynamic approach. JOURNAL OF HEALTH, POPULATION, AND NUTRITION 2024; 43:32. [PMID: 38424608 DOI: 10.1186/s41043-024-00505-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Accepted: 01/13/2024] [Indexed: 03/02/2024]
Abstract
In light of the global prevalence of a highly contagious respiratory disease, this study presents a novel approach to address the pressing and unanticipated issues by introducing a modified vaccination and lockdown-centered epidemic model. The rapid spread of the disease is attributed to viral transmissibility, the emergence of new strains (variants), lack of immunization, and human unawareness. This study aims to provide policymakers with crucial insights for making informed decisions regarding lockdown strategies, vaccine availability, and other control measures. The research adopts three types of models: deterministic, heterogeneous, and fractional-order dynamics, on both theoretical and numerical approaches. The heterogeneous network considers varying connectivity and interaction patterns among individuals, while the ABC fractional-order derivatives analyze the impact of integer-order control in different semi-groups. An extensive theoretical analysis is conducted to validate the proposed model. A comprehensive numerical investigation encompasses deterministic, stochastic, and ABC fractional-order derivatives, considering the combined effects of an effective vaccination program and non-pharmaceutical interventions, such as lockdowns and shutdowns. The findings of this research are expected to be valuable for policymakers in different countries, helping them implement dynamic strategies to control and eradicate the epidemic effectively.
Collapse
Affiliation(s)
| | | | - K M Ariful Kabir
- Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh
| |
Collapse
|
7
|
van den Ende MWJ, van der Maas HLJ, Epskamp S, Lees MH. Alcohol consumption as a socially contagious phenomenon in the Framingham Heart Study social network. Sci Rep 2024; 14:4499. [PMID: 38402289 PMCID: PMC11052543 DOI: 10.1038/s41598-024-54155-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2023] [Accepted: 02/09/2024] [Indexed: 02/26/2024] Open
Abstract
We use longitudinal social network data from the Framingham Heart Study to examine the extent to which alcohol consumption is influenced by the network structure. We assess the spread of alcohol use in a three-state SIS-type model, classifying individuals as abstainers, moderate drinkers, and heavy drinkers. We find that the use of three-states improves on the more canonical two-state classification, as the data show that all three states are highly stable and have different social dynamics. We show that when modelling the spread of alcohol use, it is important to model the topology of social interactions by incorporating the network structure. The population is not homogeneously mixed, and clustering is high with abstainers and heavy drinkers. We find that both abstainers and heavy drinkers have a strong influence on their social environment; for every heavy drinker and abstainer connection, the probability of a moderate drinker adopting their drinking behaviour increases by [Formula: see text] and [Formula: see text], respectively. We also find that abstinent connections have a significant positive effect on heavy drinkers quitting drinking. Using simulations, we find that while both are effective, increasing the influence of abstainers appears to be the more effective intervention compared to reducing the influence of heavy drinkers.
Collapse
Affiliation(s)
- Maarten W J van den Ende
- Psychological Methods, University of Amsterdam, Amsterdam, 1001 NK, The Netherlands.
- Institute of Advanced Studies, University of Amsterdam, Amsterdam, 1012 GC, The Netherlands.
| | - Han L J van der Maas
- Psychological Methods, University of Amsterdam, Amsterdam, 1001 NK, The Netherlands
| | - Sacha Epskamp
- Psychological Methods, University of Amsterdam, Amsterdam, 1001 NK, The Netherlands
- Department of Psychology, National University of Singapore, Singapore, 117570, Singapore
| | - Mike H Lees
- Institute of Advanced Studies, University of Amsterdam, Amsterdam, 1012 GC, The Netherlands
| |
Collapse
|
8
|
Oraby T, Balogh A. Modeling the effect of observational social learning on parental decision-making for childhood vaccination and diseases spread over household networks. FRONTIERS IN EPIDEMIOLOGY 2024; 3:1177752. [PMID: 38455928 PMCID: PMC10910890 DOI: 10.3389/fepid.2023.1177752] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Accepted: 12/27/2023] [Indexed: 03/09/2024]
Abstract
In this paper, we introduce a novel model for parental decision-making about vaccinations against a childhood disease that spreads through a contact network. This model considers a bilayer network comprising two overlapping networks, which are either Erdős-Rényi (random) networks or Barabási-Albert networks. The model also employs a Bayesian aggregation rule for observational social learning on a social network. This new model encompasses other decision models, such as voting and DeGroot models, as special cases. Using our model, we demonstrate how certain levels of social learning about vaccination preferences can converge opinions, influencing vaccine uptake and ultimately disease spread. In addition, we explore how two different cultures of social learning affect the establishment of social norms of vaccination and the uptake of vaccines. In every scenario, the interplay between the dynamics of observational social learning and disease spread is influenced by the network's topology, along with vaccine safety and availability.
Collapse
Affiliation(s)
- Tamer Oraby
- School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, Edinburg, TX, United States
| | | |
Collapse
|
9
|
Xiong K, Ren J, Marchesoni F, Huang J. Phononic band gap in random spring networks. Phys Rev E 2023; 108:044306. [PMID: 37978624 DOI: 10.1103/physreve.108.044306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2022] [Accepted: 09/07/2023] [Indexed: 11/19/2023]
Abstract
We investigate the relation between topological and vibrational properties of networked materials by analyzing, both numerically and analytically, the properties of a random spring network model. We establish a pseudodispersion relation, which allows us to predict the existence of distinct transitions from extended to localized vibrational modes in this class of materials. Consequently, we propose an alternative method to control phonon and elastic wave propagation in disordered networks. In particular, the phonon band gap of our spring network model can be enhanced by either increasing its average degree or decreasing its assortativity coefficient. Applications to phonon band engineering and vibrational energy harvesting are briefly discussed.
Collapse
Affiliation(s)
- Kezhao Xiong
- Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory of Micro and Nano Photonic Structures (MOE), Fudan University, Shanghai 200438, China
- College of Sciences, Xi'an University of Science and Technology, Xi'an 710054, China
| | - Jie Ren
- MOE Key Laboratory of Advanced Micro-Structured Materials and Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Fabio Marchesoni
- MOE Key Laboratory of Advanced Micro-Structured Materials and Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
- Department of Physics, University of Camerino, 62032 Camerino, Italy
| | - Jiping Huang
- Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory of Micro and Nano Photonic Structures (MOE), Fudan University, Shanghai 200438, China
| |
Collapse
|
10
|
López-Pintado D, López-Pintado S, García-Milán I, Yao Z. Uncertainty analysis of contagion processes based on a functional approach. Sci Rep 2023; 13:15522. [PMID: 37726315 PMCID: PMC10509249 DOI: 10.1038/s41598-023-42041-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2022] [Accepted: 09/04/2023] [Indexed: 09/21/2023] Open
Abstract
The spread of a disease, product or idea in a population is often hard to predict. We tend to observe one or few realizations of the contagion process and therefore limited information can be obtained for anticipating future similar events. The stochastic nature of contagion generates unpredictable outcomes throughout the whole course of the dynamics. This might lead to important inaccuracies in the predictions and to the over or under-reaction of policymakers, who tend to anticipate the average behavior. Through an extensive simulation study, we analyze properties of the contagion process, focusing on its unpredictability or uncertainty, and exploiting the functional nature of the data. In particular, we define a novel non-parametric measure of variance based on weighted depth-based central regions. We apply this methodology to the susceptible-infected-susceptible epidemiological model and small-world networks. We find that maximum uncertainty is attained at the epidemic threshold. The density of the network and the contagiousness of the process have a strong and complementary effect on the uncertainty of contagion, whereas only a mild effect of the network's randomness structure is observed.
Collapse
Affiliation(s)
| | - Sara López-Pintado
- Department of Health Sciences, Northeastern University, Boston, 02115-5005, USA.
| | - Iván García-Milán
- Engineering Department, Universidad de Loyola, 41704, Seville, Spain
| | - Zonghui Yao
- Department of Health Sciences, Northeastern University, Boston, 02115-5005, USA
| |
Collapse
|
11
|
Liu P, Li L, Wen Y, Fang S. Identifying Influential Nodes in Social Networks: Exploiting Self-Voting Mechanism. BIG DATA 2023; 11:296-306. [PMID: 37083427 DOI: 10.1089/big.2022.0165] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
The influence maximization (IM) problem is defined as identifying a group of influential nodes in a network such that these nodes can affect as many nodes as possible. Due to its great significance in viral marketing, disease control, social recommendation, and so on, considerable efforts have been devoted to the development of methods to solve the IM problem. In the literature, VoteRank and its improved algorithms have been proposed to select influential nodes based on voting approaches. However, in the voting process of these algorithms, a node cannot vote for itself. We argue that this voting schema runs counter to many real scenarios. To address this issue, we designed the VoteRank* algorithm, in which we first introduce the self-voting mechanism into the voting process. In addition, we also take into consideration the diversities of nodes. More explicitly, we measure the voting ability of nodes and the amount of a node voting for its neighbors based on the H-index of nodes. The effectiveness of the proposed algorithm is experimentally verified on 12 benchmark networks. The results demonstrate that VoteRank* is superior to the baseline methods in most cases.
Collapse
Affiliation(s)
- Panfeng Liu
- School of Information Science and Engineering, Lanzhou University, Lanzhou, China
| | - Longjie Li
- School of Information Science and Engineering, Lanzhou University, Lanzhou, China
- Key Laboratory of Media Convergence Technology and Communication, Lanzhou, China
| | - Yanhong Wen
- School of Information Science and Engineering, Lanzhou University, Lanzhou, China
| | - Shiyu Fang
- School of Information Science and Engineering, Lanzhou University, Lanzhou, China
| |
Collapse
|
12
|
Ghosh S, Khanra P, Kundu P, Ji P, Ghosh D, Hens C. Dimension reduction in higher-order contagious phenomena. CHAOS (WOODBURY, N.Y.) 2023; 33:2893033. [PMID: 37229635 DOI: 10.1063/5.0152959] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2023] [Accepted: 05/01/2023] [Indexed: 05/27/2023]
Abstract
We investigate epidemic spreading in a deterministic susceptible-infected-susceptible model on uncorrelated heterogeneous networks with higher-order interactions. We provide a recipe for the construction of one-dimensional reduced model (resilience function) of the N-dimensional susceptible-infected-susceptible dynamics in the presence of higher-order interactions. Utilizing this reduction process, we are able to capture the microscopic and macroscopic behavior of infectious networks. We find that the microscopic state of nodes (fraction of stable healthy individual of each node) inversely scales with their degree, and it becomes diminished due to the presence of higher-order interactions. In this case, we analytically obtain that the macroscopic state of the system (fraction of infectious or healthy population) undergoes abrupt transition. Additionally, we quantify the network's resilience, i.e., how the topological changes affect the stable infected population. Finally, we provide an alternative framework of dimension reduction based on the spectral analysis of the network, which can identify the critical onset of the disease in the presence or absence of higher-order interactions. Both reduction methods can be extended for a large class of dynamical models.
Collapse
Affiliation(s)
- Subrata Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Pitambar Khanra
- Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260, USA
| | - Prosenjit Kundu
- Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, Gujarat 382007, India
| | - Peng Ji
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai 200433, China
- Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (Fudan University), Ministry of Education, Shanghai 200433, China
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Chittaranjan Hens
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
- International Institute of Information Technology, Hyderabad 500 032, India
| |
Collapse
|
13
|
Granger T, Michelitsch TM, Bestehorn M, Riascos AP, Collet BA. Four-compartment epidemic model with retarded transition rates. Phys Rev E 2023; 107:044207. [PMID: 37198844 DOI: 10.1103/physreve.107.044207] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2022] [Accepted: 03/17/2023] [Indexed: 05/19/2023]
Abstract
We study an epidemic model for a constant population by taking into account four compartments of the individuals characterizing their states of health. Each individual is in one of the following compartments: susceptible S; incubated, i.e., infected yet not infectious, C; infected and infectious I; and recovered, i.e., immune, R. An infection is visible only when an individual is in state I. Upon infection, an individual performs the transition pathway S→C→I→R→S, remaining in compartments C, I, and R for a certain random waiting time t_{C}, t_{I}, and t_{R}, respectively. The waiting times for each compartment are independent and drawn from specific probability density functions (PDFs) introducing memory into the model. The first part of the paper is devoted to the macroscopic S-C-I-R-S model. We derive memory evolution equations involving convolutions (time derivatives of general fractional type). We consider several cases. The memoryless case is represented by exponentially distributed waiting times. Cases of long waiting times with fat-tailed waiting-time distributions are considered as well where the S-C-I-R-S evolution equations take the form of time-fractional ordinary differential equations. We obtain formulas for the endemic equilibrium and a condition of its existence for cases when the waiting-time PDFs have existing means. We analyze the stability of healthy and endemic equilibria and derive conditions for which the endemic state becomes oscillatory (Hopf) unstable. In the second part, we implement a simple multiple-random-walker approach (microscopic model of Brownian motion of Z independent walkers) with random S-C-I-R-S waiting times in computer simulations. Infections occur with a certain probability by collisions of walkers in compartments I and S. We compare the endemic states predicted in the macroscopic model with the numerical results of the simulations and find accordance of high accuracy. We conclude that a simple random-walker approach offers an appropriate microscopic description for the macroscopic model. The S-C-I-R-S-type models open a wide field of applications allowing the identification of pertinent parameters governing the phenomenology of epidemic dynamics such as extinction, convergence to a stable endemic equilibrium, or persistent oscillatory behavior.
Collapse
Affiliation(s)
- Téo Granger
- Sorbonne Université, Institut Jean le Rond d'Alembert, CNRS UMR 7190, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - Thomas M Michelitsch
- Sorbonne Université, Institut Jean le Rond d'Alembert, CNRS UMR 7190, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - Michael Bestehorn
- Institut für Physik, Brandenburgische Technische Universität Cottbus-Senftenberg, Erich-Weinert-Straße 1, 03046 Cottbus, Germany
| | - Alejandro P Riascos
- Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 Ciudad de México, Mexico
| | - Bernard A Collet
- Sorbonne Université, Institut Jean le Rond d'Alembert, CNRS UMR 7190, 4 Place Jussieu, 75252 Paris Cedex 05, France
| |
Collapse
|
14
|
Wanduku D. A novel complex social network rumor stochastic model: Convergence in distribution to a final rumor size. Heliyon 2023; 9:e15125. [PMID: 37077689 PMCID: PMC10106917 DOI: 10.1016/j.heliyon.2023.e15125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2022] [Revised: 10/09/2022] [Accepted: 03/27/2023] [Indexed: 04/21/2023] Open
Abstract
We introduce a chain-binomial model in a heterogeneous complex social network (HCSN) to investigate the spread of a rumor. A novel formulation of the state of the Markov chain (MC) for the SEIR (susceptible-exposed-infected-removed) rumor epidemic model is obtained, where two discrete time measures represent individuals in their disease states both instantaneously, and also the total time duration in each state. The general MC is characterized in the HCSN, for both the mean-field and global levels of the network rumor epidemic dynamics. The convergence in distribution of the MC to the final size of the rumor epidemic random variable is fully characterized. Moreover, the algorithm to obtain the expected final number of nodes that ever hear the rumor is given. An example to demonstrate the algorithm is presented.
Collapse
|
15
|
Feng M, Li X, Li Y, Li Q. The impact of nodes of information dissemination on epidemic spreading in dynamic multiplex networks. CHAOS (WOODBURY, N.Y.) 2023; 33:043112. [PMID: 37097954 DOI: 10.1063/5.0142386] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2023] [Accepted: 03/16/2023] [Indexed: 06/19/2023]
Abstract
Epidemic spreading processes on dynamic multiplex networks provide a more accurate description of natural spreading processes than those on single layered networks. To describe the influence of different individuals in the awareness layer on epidemic spreading, we propose a two-layer network-based epidemic spreading model, including some individuals who neglect the epidemic, and we explore how individuals with different properties in the awareness layer will affect the spread of epidemics. The two-layer network model is divided into an information transmission layer and a disease spreading layer. Each node in the layer represents an individual with different connections in different layers. Individuals with awareness will be infected with a lower probability compared to unaware individuals, which corresponds to the various epidemic prevention measures in real life. We adopt the micro-Markov chain approach to analytically derive the threshold for the proposed epidemic model, which demonstrates that the awareness layer affects the threshold of disease spreading. We then explore how individuals with different properties would affect the disease spreading process through extensive Monte Carlo numerical simulations. We find that individuals with high centrality in the awareness layer would significantly inhibit the transmission of infectious diseases. Additionally, we propose conjectures and explanations for the approximately linear effect of individuals with low centrality in the awareness layer on the number of infected individuals.
Collapse
Affiliation(s)
- Minyu Feng
- College of Artificial Intelligence, Southwest University, Chongqing 400715, People's Republic of China
| | - Xiangxi Li
- College of Artificial Intelligence, Southwest University, Chongqing 400715, People's Republic of China
| | - Yuhan Li
- College of Artificial Intelligence, Southwest University, Chongqing 400715, People's Republic of China
| | - Qin Li
- School of Public Policy and Administration, Chongqing University, Chongqing 400044, People's Republic of China
| |
Collapse
|
16
|
Chen L, Wang J. Bifurcation analysis in an epidemic model on adaptive networks. CHAOS (WOODBURY, N.Y.) 2023; 33:033135. [PMID: 37003833 DOI: 10.1063/5.0130068] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2022] [Accepted: 03/01/2023] [Indexed: 06/19/2023]
Abstract
In this paper, we study a delayed adaptive network epidemic model in which the local spatial connections of susceptible and susceptible individuals have time-delay effects on the rate of demographic change of local spatial connections of susceptible and susceptible individuals. We prove that the Hopf bifurcation occurs at the critical value τ0 with delay τ as the bifurcation parameter. Then, by using the normal form method and the central manifold theory, the criteria for the bifurcation direction and stability are derived. Finally, numerical simulations are presented to show the feasibility of our results.
Collapse
Affiliation(s)
- Liang Chen
- Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China
| | - JinRong Wang
- Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China
| |
Collapse
|
17
|
Zelenkovski K, Sandev T, Metzler R, Kocarev L, Basnarkov L. Random Walks on Networks with Centrality-Based Stochastic Resetting. ENTROPY (BASEL, SWITZERLAND) 2023; 25:293. [PMID: 36832659 PMCID: PMC9955709 DOI: 10.3390/e25020293] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/26/2022] [Revised: 01/19/2023] [Accepted: 02/02/2023] [Indexed: 06/18/2023]
Abstract
We introduce a refined way to diffusely explore complex networks with stochastic resetting where the resetting site is derived from node centrality measures. This approach differs from previous ones, since it not only allows the random walker with a certain probability to jump from the current node to a deliberately chosen resetting node, rather it enables the walker to jump to the node that can reach all other nodes faster. Following this strategy, we consider the resetting site to be the geometric center, the node that minimizes the average travel time to all the other nodes. Using the established Markov chain theory, we calculate the Global Mean First Passage Time (GMFPT) to determine the search performance of the random walk with resetting for different resetting node candidates individually. Furthermore, we compare which nodes are better resetting node sites by comparing the GMFPT for each node. We study this approach for different topologies of generic and real-life networks. We show that, for directed networks extracted for real-life relationships, this centrality focused resetting can improve the search to a greater extent than for the generated undirected networks. This resetting to the center advocated here can minimize the average travel time to all other nodes in real networks as well. We also present a relationship between the longest shortest path (the diameter), the average node degree and the GMFPT when the starting node is the center. We show that, for undirected scale-free networks, stochastic resetting is effective only for networks that are extremely sparse with tree-like structures as they have larger diameters and smaller average node degrees. For directed networks, the resetting is beneficial even for networks that have loops. The numerical results are confirmed by analytic solutions. Our study demonstrates that the proposed random walk approach with resetting based on centrality measures reduces the memoryless search time for targets in the examined network topologies.
Collapse
Affiliation(s)
- Kiril Zelenkovski
- Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, 1000 Skopje, Macedonia
| | - Trifce Sandev
- Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, 1000 Skopje, Macedonia
- Institute of Physics, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University, Arhimedova 3, 1000 Skopje, Macedonia
- Institute of Physics & Astronomy, University of Potsdam, D-14776 Potsdam, Germany
| | - Ralf Metzler
- Institute of Physics & Astronomy, University of Potsdam, D-14776 Potsdam, Germany
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
| | - Ljupco Kocarev
- Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, 1000 Skopje, Macedonia
- Faculty of Computer Science and Engineering, Ss. Cyril and Methodius University, 1000 Skopje, Macedonia
| | - Lasko Basnarkov
- Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, 1000 Skopje, Macedonia
- Faculty of Computer Science and Engineering, Ss. Cyril and Methodius University, 1000 Skopje, Macedonia
| |
Collapse
|
18
|
Huo L, Meng S. Effect of decay behavior of information on disease dissemination in multiplex network. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:4516-4531. [PMID: 36896510 DOI: 10.3934/mbe.2023209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
The diseases dissemination always brings serious problems in the economy and livelihood issues. It is necessary to study the law of disease dissemination from multiple dimensions. Information quality about disease prevention has a great impact on the dissemination of disease, that is because only the real information can inhibit the dissemination of disease. In fact, the dissemination of information involves the decay of the amount of real information and the information quality becomes poor gradually, which will affect the individual's attitude and behavior towards disease. In order to study the influence of the decay behavior of information on disease dissemination, in the paper, an interaction model between information and disease dissemination is established to describe the effect of the decay behavior of information on the coupled dynamics of process in multiplex network. According to the mean-field theory, the threshold condition of disease dissemination is derived. Finally, through theoretical analysis and numerical simulation, some results can be obtained. The results show that decay behavior is a factor that greatly affects the disease dissemination and can change the final size of disease dissemination. The larger the decay constant, the smaller final size of disease dissemination. In the process of information dissemination, emphasizing key information can reduce the impact of decay behavior.
Collapse
Affiliation(s)
- Liang'an Huo
- Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
| | - Shiguang Meng
- Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
| |
Collapse
|
19
|
Pei H, Yan G, Huang Y. Impact of contact rate on epidemic spreading in complex networks. THE EUROPEAN PHYSICAL JOURNAL. B 2023; 96:44. [PMID: 37041759 PMCID: PMC10078040 DOI: 10.1140/epjb/s10051-023-00513-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/07/2023] [Accepted: 03/27/2023] [Indexed: 05/17/2023]
Abstract
Abstract Contact reduction is an effective strategy to mitigate the spreading of epidemic. However, the existing reaction-diffusion equations for infectious disease are unable to characterize this effect. Thus, we here propose an extended susceptible-infected-recovered model by incorporating contact rate into the standard SIR model, and concentrate on investigating its impact on epidemic transmission. We analytically derive the epidemic thresholds on homogeneous and heterogeneous networks, respectively. The effects of contact rate on spreading speed, scale and outbreak threshold are explored on ER and SF networks. Simulations results show that epidemic dissemination is significantly mitigated when contact rate is reduced. Importantly, epidemic spreads faster on heterogeneous networks while broader on homogeneous networks, and the outbreak thresholds of the former are smaller. Graphical abstract
Collapse
Affiliation(s)
- Huayan Pei
- School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou, 730070 Gansu China
- Key Laboratory of Media Convergence Technology and Communication, Lanzhou, 730030 Gansu China
| | - Guanghui Yan
- School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou, 730070 Gansu China
- Key Laboratory of Media Convergence Technology and Communication, Lanzhou, 730030 Gansu China
| | - Yaning Huang
- Key Laboratory of Media Convergence Technology and Communication, Lanzhou, 730030 Gansu China
- Gansu Daily Newspaper Industry Group, Lanzhou, 730030 Gansu China
| |
Collapse
|
20
|
Lee MJ, Kim JH, Goh KI, Lee SH, Son SW, Lee DS. Degree distributions under general node removal: Power-law or Poisson? Phys Rev E 2022; 106:064309. [PMID: 36671153 DOI: 10.1103/physreve.106.064309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Accepted: 11/01/2022] [Indexed: 06/17/2023]
Abstract
Perturbations made to networked systems may result in partial structural loss, such as a blackout in a power-grid system. Investigating the resulting disturbance in network properties is quintessential to understand real networks in action. The removal of nodes is a representative disturbance, but previous studies are seemingly contrasting about its effect on arguably the most fundamental network statistic, the degree distribution. The key question is about the functional form of the degree distributions that can be altered during node removal or sampling. The functional form is decisive in the remaining subnetwork's static and dynamical properties. In this work, we clarify the situation by utilizing the relative entropies with respect to the reference distributions in the Poisson and power-law form, to quantify the distance between the subnetwork's degree distribution and either of the reference distributions. Introducing general sequential node removal processes with continuously different levels of hub protection to encompass a series of scenarios including uniform random removal and preferred or protective (i.e., biased random) removal of the hub, we classify the altered degree distributions starting from various power-law forms by comparing two relative entropy values. From the extensive investigation in various scenarios based on direct node-removal simulations and by solving the rate equation of degree distributions, we discover in the parameter space two distinct regimes, one where the degree distribution is closer to the power-law reference distribution and the other closer to the Poisson distribution.
Collapse
Affiliation(s)
- Mi Jin Lee
- Department of Applied Physics, Hanyang University, Ansan 15588, Korea
| | - Jung-Ho Kim
- Department of Physics, Korea University, Seoul 02841, Korea
| | - Kwang-Il Goh
- Department of Physics, Korea University, Seoul 02841, Korea
| | - Sang Hoon Lee
- Department of Physics and Research Institute of Natural Science, Gyeongsang National University, Jinju 52828, Korea
- Future Convergence Technology Research Institute, Gyeongsang National University, Jinju 52849, Korea
| | - Seung-Woo Son
- Department of Applied Physics, Hanyang University, Ansan 15588, Korea
| | - Deok-Sun Lee
- School of Computational Sciences and Center for AI and Natural Sciences, Korea Institute for Advanced Study, Seoul 02455, Korea
| |
Collapse
|
21
|
Sheikhahmadi A, Veisi F, Sheikhahmadi A, Mohammadimajd S. A multi-attribute method for ranking influential nodes in complex networks. PLoS One 2022; 17:e0278129. [PMID: 36441805 PMCID: PMC9704601 DOI: 10.1371/journal.pone.0278129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Accepted: 11/09/2022] [Indexed: 11/29/2022] Open
Abstract
Calculating the importance of influential nodes and ranking them based on their diffusion power is one of the open issues and critical research fields in complex networks. It is essential to identify an attribute that can compute and rank the diffusion power of nodes with high accuracy, despite the plurality of nodes and many relationships between them. Most methods presented only use one structural attribute to capture the influence of individuals, which is not entirely accurate in most networks. The reason is that network structures are disparate, and these methods will be inefficient by altering the network. A possible solution is to use more than one attribute to examine the characteristics aspect and address the issue mentioned. Therefore, this study presents a method for identifying and ranking node's ability to spread information. The purpose of this study is to present a multi-attribute decision making approach for determining diffusion power and classification of nodes, which uses several local and semi-local attributes. Local and semi-local attributes with linear time complexity are used, considering different aspects of the network nodes. Evaluations performed on datasets of real networks demonstrate that the proposed method performs satisfactorily in allocating distinct ranks to nodes; moreover, as the infection rate of nodes increases, the accuracy of the proposed method increases.
Collapse
Affiliation(s)
- Adib Sheikhahmadi
- Department of Computer Engineering, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran
| | - Farshid Veisi
- Department of Computer Engineering, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran
| | - Amir Sheikhahmadi
- Department of Computer Engineering, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran
- * E-mail:
| | | |
Collapse
|
22
|
Ito H, Shigeta K, Yamamoto T, Morita S. Exploring sexual contact networks by analyzing a nationwide commercial-sex review website. PLoS One 2022; 17:e0276981. [PMID: 36327305 PMCID: PMC9632804 DOI: 10.1371/journal.pone.0276981] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2022] [Accepted: 10/18/2022] [Indexed: 11/06/2022] Open
Abstract
Understanding the structure of human sexual contact networks is vital in a broad range of disciplines, including sociology, biology, public health, and anthropology. However, sexual contact networks are yet to be understood because technical and privacy issues make it difficult to conduct accurate, large-scale surveys. In this study, we surveyed data openly available on one of the largest adult entertainment websites in Japan, where male clients (MCs) can write online customer reviews of female commercial sex workers (FCSWs). In particular, our investigation focused on a type of establishment called "soapland," the only type of sex industry in Japan where sexual intercourse is publicly permitted. Soaplands are scattered throughout Japan, and the study website covers approximately 66% of them. Using such a vast amount of data on a nationwide scale, we clarified the network structure of commercial sex, characterized by small-world, scale-free, and disassortative mating properties. To study geographical characteristics, we compared the resulting network with three different artificially generated networks via the random rewiring of links. Moreover, we considered a simple epidemic model on the resulting network, and investigated whether it would be more effective to provide infection control measures to FCSWs or MCs. We determined that active FCSWs constitute an important pathway of infection propagation in commercial sex networks, but MCs also play an essential role as weak ties.
Collapse
Affiliation(s)
- Hiromu Ito
- Department of International Health and Medical Anthropology, Institute of Tropical Medicine, Nagasaki University, Nagasaki, Japan
| | - Keiko Shigeta
- Department of International Health and Medical Anthropology, Institute of Tropical Medicine, Nagasaki University, Nagasaki, Japan
| | - Taro Yamamoto
- Department of International Health and Medical Anthropology, Institute of Tropical Medicine, Nagasaki University, Nagasaki, Japan
| | - Satoru Morita
- Department of Mathematical and Systems Engineering, Shizuoka University, Hamamatsu, Shizuoka, Japan
- * E-mail:
| |
Collapse
|
23
|
Abstract
Abstract
We study a stochastic compartmental susceptible–infected (SI) epidemic process on a configuration model random graph with a given degree distribution over a finite time interval. We split the population of graph vertices into two compartments, namely, S and I, denoting susceptible and infected vertices, respectively. In addition to the sizes of these two compartments, we keep track of the counts of SI-edges (those connecting a susceptible and an infected vertex) and SS-edges (those connecting two susceptible vertices). We describe the dynamical process in terms of these counts and present a functional central limit theorem (FCLT) for them as the number of vertices in the random graph grows to infinity. The FCLT asserts that the counts, when appropriately scaled, converge weakly to a continuous Gaussian vector semimartingale process in the space of vector-valued càdlàg functions endowed with the Skorokhod topology. We discuss applications of the FCLT in percolation theory and in modelling the spread of computer viruses. We also provide simulation results illustrating the FCLT for some common degree distributions.
Collapse
|
24
|
Mizutaka S, Mori K, Hasegawa T. Synergistic epidemic spreading in correlated networks. Phys Rev E 2022; 106:034305. [PMID: 36266882 DOI: 10.1103/physreve.106.034305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Accepted: 08/04/2022] [Indexed: 06/16/2023]
Abstract
We investigate the effect of degree correlation on a susceptible-infected-susceptible (SIS) model with a nonlinear cooperative effect (synergy) in infectious transmissions. In a mean-field treatment of the synergistic SIS model on a bimodal network with tunable degree correlation, we identify a discontinuous transition that is independent of the degree correlation strength unless the synergy is absent or extremely weak. Regardless of synergy (absent or present), a positive and negative degree correlation in the model reduces and raises the epidemic threshold, respectively. For networks with a strongly positive degree correlation, the mean-field treatment predicts the emergence of two discontinuous jumps in the steady-state infected density. To test the mean-field treatment, we provide approximate master equations of the present model. We quantitatively confirm that the approximate master equations agree with not only all qualitative predictions of the mean-field treatment but also corresponding Monte Carlo simulations.
Collapse
Affiliation(s)
- Shogo Mizutaka
- Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi 924-1292, Japan
| | - Kizashi Mori
- Graduate School of Science and Engineering, Ibaraki University, 2-1-1 Bunkyo, Mito 310-8512, Japan
| | - Takehisa Hasegawa
- Graduate School of Science and Engineering, Ibaraki University, 2-1-1 Bunkyo, Mito 310-8512, Japan
| |
Collapse
|
25
|
Huo L, Zhao R, Zhao L. Effects of official information and rumor on resource-epidemic coevolution dynamics. JOURNAL OF KING SAUD UNIVERSITY - COMPUTER AND INFORMATION SCIENCES 2022. [PMID: 37521178 PMCID: PMC9452419 DOI: 10.1016/j.jksuci.2022.09.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
Abstract
Epidemic-related information and resources have proven to have a significant impact on the spread of the epidemic during the Corona Virus Disease 2019 (COVID-19) pandemic. The various orientation role of information has different effects on the epidemic spreading process, which will affect the individual’ awareness of resources allocation and epidemic spreading scale. Based on this, a three-layer network is established to describe the dynamic coevolution process among information dissemination, resource allocation, and epidemic spreading. In order to analyze dynamic coevolution process, the microscopic Markov chain (MMC) theory is used. Then, the threshold of epidemic spreading is deduced. Our results indicated that the official information orientation intensity inhibits the epidemics spreading, while rumor orientation intensity promotes epidemic spreading. At the same time, the efficiency of resource utilization restrains the expansion of the infection scale. The two kinds of information are combined with resources respectively. Official information will enhance the inhibitory effect of resources epidemics spreading, while rumor will do the opposite.
Collapse
|
26
|
Fan C, Jiang X, Lee R, Mostafavi A. Data-driven contact network models of COVID-19 reveal trade-offs between costs and infections for optimal local containment policies. CITIES (LONDON, ENGLAND) 2022; 128:103805. [PMID: 35694433 PMCID: PMC9174357 DOI: 10.1016/j.cities.2022.103805] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/09/2021] [Revised: 11/29/2021] [Accepted: 06/02/2022] [Indexed: 06/15/2023]
Abstract
While several non-pharmacological measures have been implemented for a few months in an effort to slow the coronavirus disease (COVID-19) pandemic in the United States, the disease remains a danger in a number of counties as restrictions are lifted to revive the economy. Making a trade-off between economic recovery and infection control is a major challenge confronting many hard-hit counties. Understanding the transmission process and quantifying the costs of local policies are essential to the task of tackling this challenge. Here, we investigate the dynamic contact patterns of the populations from anonymized, geo-localized mobility data and census and demographic data to create data-driven, agent-based contact networks. We then simulate the epidemic spread with a time-varying contagion model in ten large metropolitan counties in the United States and evaluate a combination of mobility reduction, mask use, and reopening policies. We find that our model captures the spatial-temporal and heterogeneous case trajectory within various counties based on dynamic population behaviors. Our results show that a decision-making tool that considers both economic cost and infection outcomes of policies can be informative in making decisions of local containment strategies for optimal balancing of economic slowdown and virus spread.
Collapse
Affiliation(s)
- Chao Fan
- Zachry Department of Civil and Environmental Engineering, Texas A&M University, College Station, TX 77843-3136, United States of America
| | - Xiangqi Jiang
- Department of Computer Science and Engineering, Texas A&M University, College Station, TX 77843-3112, United States of America
| | - Ronald Lee
- Department of Computer Science and Engineering, Texas A&M University, College Station, TX 77843-3112, United States of America
| | - Ali Mostafavi
- Zachry Department of Civil and Environmental Engineering, Texas A&M University, College Station, TX 77843-3136, United States of America
| |
Collapse
|
27
|
Jhun B, Choi H. Abrupt transition of the efficient vaccination strategy in a population with heterogeneous fatality rates. CHAOS (WOODBURY, N.Y.) 2022; 32:093140. [PMID: 36182386 DOI: 10.1063/5.0087627] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2022] [Accepted: 09/01/2022] [Indexed: 06/16/2023]
Abstract
An insufficient supply of an effective SARS-CoV-2 vaccine in most countries demands an effective vaccination strategy to minimize the damage caused by the disease. Currently, many countries vaccinate their population in descending order of age (i.e., descending order of fatality rate) to minimize the deaths caused by the disease; however, the effectiveness of this strategy needs to be quantitatively assessed. We employ the susceptible-infected-recovered-dead model to investigate various vaccination strategies. We constructed a metapopulation model with heterogeneous contact and fatality rates and investigated the effectiveness of vaccination strategies to reduce epidemic mortality. We found that the fatality-based strategy, which is currently employed in many countries, is more effective when the contagion rate is high and vaccine supply is low, but the contact-based method outperforms the fatality-based strategy when there is a sufficiently high supply of the vaccine. We identified a discontinuous transition of the optimal vaccination strategy and path-dependency analogous to hysteresis. This transition and path-dependency imply that combining the fatality-based and contact-based strategies is ineffective in reducing the number of deaths. Furthermore, we demonstrate that such phenomena occur in real-world epidemic diseases, such as tuberculosis and COVID-19. We also show that the conclusions of this research are valid even when the complex epidemic stages, efficacy of the vaccine, and reinfection are considered.
Collapse
Affiliation(s)
- Bukyoung Jhun
- CCSS, CTP, and Department of Physics and Astronomy, Seoul National University, Seoul 08826, South Korea
| | - Hoyun Choi
- CCSS, CTP, and Department of Physics and Astronomy, Seoul National University, Seoul 08826, South Korea
| |
Collapse
|
28
|
Cattle transport network predicts endemic and epidemic foot-and-mouth disease risk on farms in Turkey. PLoS Comput Biol 2022; 18:e1010354. [PMID: 35984841 PMCID: PMC9432692 DOI: 10.1371/journal.pcbi.1010354] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2021] [Revised: 08/31/2022] [Accepted: 07/03/2022] [Indexed: 11/19/2022] Open
Abstract
The structure of contact networks affects the likelihood of disease spread at the population scale and the risk of infection at any given node. Though this has been well characterized for both theoretical and empirical networks for the spread of epidemics on completely susceptible networks, the long-term impact of network structure on risk of infection with an endemic pathogen, where nodes can be infected more than once, has been less well characterized. Here, we analyze detailed records of the transportation of cattle among farms in Turkey to characterize the global and local attributes of the directed—weighted shipments network between 2007-2012. We then study the correlations between network properties and the likelihood of infection with, or exposure to, foot-and-mouth disease (FMD) over the same time period using recorded outbreaks. The shipments network shows a complex combination of features (local and global) that have not been previously reported in other networks of shipments; i.e. small-worldness, scale-freeness, modular structure, among others. We find that nodes that were either infected or at high risk of infection with FMD (within one link from an infected farm) had disproportionately higher degree, were more central (eigenvector centrality and coreness), and were more likely to be net recipients of shipments compared to those that were always more than 2 links away from an infected farm. High in-degree (i.e. many shipments received) was the best univariate predictor of infection. Low in-coreness (i.e. peripheral nodes) was the best univariate predictor of nodes always more than 2 links away from an infected farm. These results are robust across the three different serotypes of FMD observed in Turkey and during periods of low-endemic prevalence and high-prevalence outbreaks. Contact network epidemiology has been extensively used in the context of infectious diseases, primarily focusing on epidemic diseases. In this paper we use detailed recorded data about cattle exchange between farms in Turkey from 2007 to 2012, to build, analyze and characterize the directed-weighted complex network of shipments of cattle. Additionally, using outbreaks data about recorded cases of foot-and-mouth disease (FMD) in Turkey, we assess the correlation between the “farm’s” position in the network (importance) and the risk of being infected with FMD, which has been endemic in Turkey for a long time. We find some network measures that are more likely to identify high-risk and low-risk farms (in-degree and in-coreness, respectively) when proposing strategies for surveillance or containment of an infectious disease.
Collapse
|
29
|
Hâncean MG, Lerner J, Perc M, Oană I, Bunaciu DA, Stoica AA, Ghiţă MC. Occupations and their impact on the spreading of COVID-19 in urban communities. Sci Rep 2022; 12:14115. [PMID: 35982107 PMCID: PMC9387884 DOI: 10.1038/s41598-022-18392-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2021] [Accepted: 08/10/2022] [Indexed: 11/09/2022] Open
Abstract
The current pandemic has disproportionally affected the workforce. To improve our understanding of the role that occupations play in the transmission of COVID-19, we analyse real-world network data that were collected in Bucharest between August 1st and October 31st 2020. The data record sex, age, and occupation of 6895 patients and the 13,272 people they have interacted with, thus providing a social network from an urban setting through which COVID-19 has spread. Quite remarkably, we find that medical occupations have no significant effect on the spread of the virus. Instead, we find common transmission chains to start with infected individuals who hold jobs in the private sector and are connected with non-active alters, such as spouses, siblings, or elderly relatives. We use relational hyperevent models to assess the most likely homophily and network effects in the community transmission. We detect homophily with respect to age and anti-homophily with respect to sex and employability. We note that, although additional data would be welcomed to perform more in-depth network analyses, our findings may help public authorities better target under-performing vaccination campaigns.
Collapse
Affiliation(s)
- Marian-Gabriel Hâncean
- Department of Sociology, University of Bucharest, Panduri 90-92, 050663, Bucharest, Romania.
| | - Jürgen Lerner
- Department of Computer and Information Science, University of Konstanz, 78457, Konstanz, Germany.,Human Technology Center, RWTH Aachen University, 52062, Aachen, Germany
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000, Maribor, Slovenia.,Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 404332, Taiwan.,Alma Mater Europaea, Slovenska ulica 17, 2000, Maribor, Slovenia.,Complexity Science Hub Vienna, Josefstädterstraße 39, 1080, Vienna, Austria
| | - Iulian Oană
- Department of Sociology, University of Bucharest, Panduri 90-92, 050663, Bucharest, Romania
| | - David-Andrei Bunaciu
- Department of Sociology, University of Bucharest, Panduri 90-92, 050663, Bucharest, Romania
| | | | - Maria-Cristina Ghiţă
- Department of Sociology, University of Bucharest, Panduri 90-92, 050663, Bucharest, Romania
| |
Collapse
|
30
|
Jain L. An entropy-based method to control COVID-19 rumors in online social networks using opinion leaders. TECHNOLOGY IN SOCIETY 2022; 70:102048. [PMID: 35765463 PMCID: PMC9222031 DOI: 10.1016/j.techsoc.2022.102048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/24/2022] [Revised: 06/19/2022] [Accepted: 06/20/2022] [Indexed: 06/15/2023]
Abstract
- In the ongoing COVID-19 pandemic, people spread various COVID-19-related rumors and hoaxes that negatively influence human civilization through online social networks (OSN). The proposed research addresses the unique and innovative approach to controlling COVID-19 rumors through the power of opinion leaders (OLs) in OSN. The entire process is partitioned into two phases; the first phase describes the novel Reputation-based Opinion Leader Identification (ROLI) algorithm, including a unique voting method to identify the top-T OLs in the OSN. The second phase describes the technique to measure the aggregated polarity score of each posted tweet/post and compute each user's reputation. The empirical reputation is utilized to calculate the user's trust, the post's entropy, and its veracity. If the experimental entropy of the post is lower than the empirical threshold value, the post is likely to be categorized as a rumor. The proposed approach operated on Twitter, Instagram, and Reddit social networks for validation. The ROLI algorithm provides 91% accuracy, 93% precision, 95% recall, and 94% F1-score over other Social Network Analysis (SNA) measures to find OLs in OSN. Moreover, the proposed approach's rumor controlling effectiveness and efficiency is also estimated based on three standard metrics; affected degree, represser degree, and diffuser degree, and obtained 26%, 22%, and 23% improvement, respectively. The concluding outcomes illustrate that the influence of OLs is exceptionally significant in controlling COVID-19 rumors.
Collapse
Affiliation(s)
- Lokesh Jain
- Department of Computer Science & Engineering, India
- Delhi Technological University, New Delhi, India
| |
Collapse
|
31
|
Tomovski I, Basnarkov L, Abazi A. Endemic state equivalence between non-Markovian SEIS and Markovian SIS model in complex networks. PHYSICA A 2022; 599:127480. [PMID: 35529899 PMCID: PMC9055791 DOI: 10.1016/j.physa.2022.127480] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/13/2022] [Revised: 04/21/2022] [Indexed: 06/14/2023]
Abstract
In the light of several major epidemic events that emerged in the past two decades, and emphasized by the COVID-19 pandemics, the non-Markovian spreading models occurring on complex networks gained significant attention from the scientific community. Following this interest, in this article, we explore the relations that exist between the mean-field approximated non-Markovian SEIS (Susceptible-Exposed-Infectious-Susceptible) and the classical Markovian SIS, as basic reoccurring virus spreading models in complex networks. We investigate the similarities and seek for equivalences both for the discrete-time and the continuous-time forms. First, we formally introduce the continuous-time non-Markovian SEIS model, and derive the epidemic threshold in a strict mathematical procedure. Then we present the main result of the paper that, providing certain relations between process parameters hold, the stationary-state solutions of the status probabilities in the non-Markovian SEIS may be found from the stationary state probabilities of the Markovian SIS model. This result has a two-fold significance. First, it simplifies the computational complexity of the non-Markovian model in practical applications, where only the stationary distributions of the state probabilities are required. Next, it defines the epidemic threshold of the non-Markovian SEIS model, without the necessity of a thrall mathematical analysis. We present this result both in analytical form, and confirm the result through numerical simulations. Furthermore, as of secondary importance, in an analytical procedure we show that each Markovian SIS may be represented as non-Markovian SEIS model.
Collapse
Affiliation(s)
- Igor Tomovski
- Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov, 2, P.O. Box 428, 1000 Skopje, Macedonia
| | - Lasko Basnarkov
- Faculty of Computer Science and Engineering, "Ss Cyril and Methodius" University - Skopje, ul.Rudzer Boshkovikj 16, P.O. Box 393, 1000 Skopje, Macedonia
- Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov, 2, P.O. Box 428, 1000 Skopje, Macedonia
| | - Alajdin Abazi
- Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov, 2, P.O. Box 428, 1000 Skopje, Macedonia
- South East European University, Ilindenska n.335, 1200 Tetovo, Macedonia
| |
Collapse
|
32
|
Kundu P, MacLaren NG, Kori H, Masuda N. Mean-field theory for double-well systems on degree-heterogeneous networks. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2022.0350] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Many complex dynamical systems in the real world, including ecological, climate, financial and power-grid systems, often show critical transitions, or tipping points, in which the system’s dynamics suddenly transit into a qualitatively different state. In mathematical models, tipping points happen as a control parameter gradually changes and crosses a certain threshold. Tipping elements in such systems may interact with each other as a network, and understanding the behaviour of interacting tipping elements is a challenge because of the high dimensionality originating from the network. Here, we develop a degree-based mean-field theory for a prototypical double-well system coupled on a network with the aim of understanding coupled tipping dynamics with a low-dimensional description. The method approximates both the onset of the tipping point and the position of equilibria with a reasonable accuracy. Based on the developed theory and numerical simulations, we also provide evidence for multistage tipping point transitions in networks of double-well systems.
Collapse
Affiliation(s)
- Prosenjit Kundu
- Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA
| | - Neil G. MacLaren
- Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA
| | - Hiroshi Kori
- Department of Complexity Science and Engineering, The University of Tokyo, Chiba 277-8561, Japan
| | - Naoki Masuda
- Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA
- Computational and Data-Enabled Science and Engineering Program, State University of New York at Buffalo, Buffalo, NY 14260-5030, USA
- Faculty of Science and Engineering, Waseda University, Tokyo 169-8555, Japan
| |
Collapse
|
33
|
Wang H, Zhang HF, Zhu PC, Ma C. Interplay of simplicial awareness contagion and epidemic spreading on time-varying multiplex networks. CHAOS (WOODBURY, N.Y.) 2022; 32:083110. [PMID: 36049933 DOI: 10.1063/5.0099183] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2022] [Accepted: 07/14/2022] [Indexed: 06/15/2023]
Abstract
There has been growing interest in exploring the dynamical interplay of epidemic spreading and awareness diffusion within the multiplex network framework. Recent studies have demonstrated that pairwise interactions are not enough to characterize social contagion processes, but the complex mechanisms of influence and reinforcement should be considered. Meanwhile, the physical social interaction of individuals is not static but time-varying. Therefore, we propose a novel sUAU-tSIS model to characterize the interplay of simplicial awareness contagion and epidemic spreading on time-varying multiplex networks, in which one layer with 2-simplicial complexes is considered the virtual information layer to address the complex contagion mechanisms in awareness diffusion and the other layer with time-varying and memory effects is treated as the physical contact layer to mimic the temporal interaction pattern among population. The microscopic Markov chain approach based theoretical analysis is developed, and the epidemic threshold is also derived. The experimental results show that our theoretical method is in good agreement with the Monte Carlo simulations. Specifically, we find that the synergistic reinforcement mechanism coming from the group interactions promotes the diffusion of awareness, leading to the suppression of the spreading of epidemics. Furthermore, our results illustrate that the contact capacity of individuals, activity heterogeneity, and memory strength also play important roles in the two dynamics; interestingly, a crossover phenomenon can be observed when investigating the effects of activity heterogeneity and memory strength.
Collapse
Affiliation(s)
- Huan Wang
- The Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematical Science, Anhui University, Hefei 230601, China
| | - Hai-Feng Zhang
- The Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematical Science, Anhui University, Hefei 230601, China
| | - Pei-Can Zhu
- School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University (NWPU), Xi'an 710072, Shaanxi, China
| | - Chuang Ma
- School of Internet, Anhui University, Hefei 230601, China
| |
Collapse
|
34
|
Warambhe MC, Deshmukh AD, Gade PM. Absorbing phase transition in a unidirectionally coupled layered network. Phys Rev E 2022; 106:014303. [PMID: 35974497 DOI: 10.1103/physreve.106.014303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2021] [Accepted: 06/22/2022] [Indexed: 06/15/2023]
Abstract
We study the contact process on layered networks in which each layer is unidirectionally coupled to the next layer. Each layer has elements sitting on (i) an Erdös-Réyni network, and (ii) a d-dimensional lattice. The top layer is not connected to any layer and undergoes an absorbing transition in the directed percolation class for the corresponding topology. The critical infection probability p_{c} for the transition is the same for all layers. For an Erdös-Réyni network the order parameter decays as t^{-δ_{l}} at p_{c} for the lth layer with δ_{l}∼2^{1-l}. This can be explained with a hierarchy of differential equations in the mean-field approximation. The dynamic exponent z=0.5 for all layers and ν_{∥}→2 for larger l. For a d-dimensional lattice, we observe a stretched exponential decay of the order parameter for all but the top layer at p_{c}.
Collapse
Affiliation(s)
- Manoj C Warambhe
- Department of Physics, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur 440033, India
| | - Ankosh D Deshmukh
- Department of Physics, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur 440033, India
| | - Prashant M Gade
- Department of Physics, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur 440033, India
| |
Collapse
|
35
|
Herd immunity under individual variation and reinfection. J Math Biol 2022; 85:2. [PMID: 35773525 PMCID: PMC9246817 DOI: 10.1007/s00285-022-01771-x] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2021] [Revised: 05/09/2022] [Accepted: 06/10/2022] [Indexed: 11/04/2022]
Abstract
We study a susceptible-exposed-infected-recovered (SEIR) model considered by Aguas et al. (In: Herd immunity thresholds for SARS-CoV-2 estimated from unfolding epidemics, 2021), Gomes et al. (In: J Theor Biol. 540:111063, 2022) where individuals are assumed to differ in their susceptibility or exposure to infection. Under this heterogeneity assumption, epidemic growth is effectively suppressed when the percentage of the population having acquired immunity surpasses a critical level - the herd immunity threshold - that is lower than in homogeneous populations. We derive explicit formulas to calculate herd immunity thresholds and stable configurations, especially when susceptibility or exposure are gamma distributed, and explore extensions of the model.
Collapse
|
36
|
Gomes MGM, Ferreira MU, Corder RM, King JG, Souto-Maior C, Penha-Gonçalves C, Gonçalves G, Chikina M, Pegden W, Aguas R. Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold. J Theor Biol 2022; 540:111063. [PMID: 35189135 PMCID: PMC8855661 DOI: 10.1016/j.jtbi.2022.111063] [Citation(s) in RCA: 33] [Impact Index Per Article: 16.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2021] [Revised: 02/14/2022] [Accepted: 02/15/2022] [Indexed: 12/21/2022]
Abstract
Individual variation in susceptibility and exposure is subject to selection by natural infection, accelerating the acquisition of immunity, and reducing herd immunity thresholds and epidemic final sizes. This is a manifestation of a wider population phenomenon known as "frailty variation". Despite theoretical understanding, public health policies continue to be guided by mathematical models that leave out considerable variation and as a result inflate projected disease burdens and overestimate the impact of interventions. Here we focus on trajectories of the coronavirus disease (COVID-19) pandemic in England and Scotland until November 2021. We fit models to series of daily deaths and infer relevant epidemiological parameters, including coefficients of variation and effects of non-pharmaceutical interventions which we find in agreement with independent empirical estimates based on contact surveys. Our estimates are robust to whether the analysed data series encompass one or two pandemic waves and enable projections compatible with subsequent dynamics. We conclude that vaccination programmes may have contributed modestly to the acquisition of herd immunity in populations with high levels of pre-existing naturally acquired immunity, while being crucial to protect vulnerable individuals from severe outcomes as the virus becomes endemic.
Collapse
Affiliation(s)
- M Gabriela M Gomes
- Department of Mathematics and Statistics, University of Strathclyde, Glasgow, UK; Centro de Matemática e Aplicações, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal
| | - Marcelo U Ferreira
- Institute of Biomedical Sciences, University of São Paulo, São Paulo, Brazil; Global Health and Tropical Medicine, Institute of Hygiene and Tropical Medicine, Nova University of Lisbon, Lisbon, Portugal
| | - Rodrigo M Corder
- Institute of Biomedical Sciences, University of São Paulo, São Paulo, Brazil
| | - Jessica G King
- Institute of Evolutionary Biology, University of Edinburgh, Edinburgh, UK
| | - Caetano Souto-Maior
- Laboratory of Systems Genetics, National Heart Lung and Blood Institute, National Institutes of Health, Bethesda, MD, USA
| | | | - Guilherme Gonçalves
- Unidade Multidisciplinar de Investigação Biomédica, Instituto de Ciências Biomédicas Abel Salazar, Universidade do Porto, Porto, Portugal
| | - Maria Chikina
- Department of Computational and Systems Biology, University of Pittsburgh, Pittburgh, PA, USA
| | - Wesley Pegden
- Department of Mathematical Sciences, Carnegie Mellon University, Pittburgh, PA, USA
| | - Ricardo Aguas
- Centre for Tropical Medicine and Global Health, Nuffield Department of Medicine, University of Oxford, Oxford, UK
| |
Collapse
|
37
|
Huang YJ, Hsiao AT, Juang J. Incorporating economic constraints for optimal control of immunizing infections. CHAOS (WOODBURY, N.Y.) 2022; 32:053101. [PMID: 35649982 DOI: 10.1063/5.0083312] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2021] [Accepted: 04/11/2022] [Indexed: 06/15/2023]
Abstract
It is well-known that the interruption of transmission of a disease can be achieved, provided the vaccinated population reaches a threshold depending on, among others, the efficacy of vaccines. The purpose of this paper is to address the optimal vaccination strategy by imposing the economic constraints. In particular, an S--(I,V)--S model used to describe the spreading of the disease in a well-mixed population and a cost function consisting of vaccination and infection costs are proposed. The well-definedness of the above-described modeling is provided. We were then able to provide an optimal strategy to minimize the cost for all parameters. In particular, the optimal vaccination level to minimize the cost can be completely characterized for all parameters. For instance, the optimal vaccination level can be classified by the magnitude of the failure rate of the vaccine with other parameters being given. Under these circumstances, the optimal strategy to minimize the cost is roughly to eliminate the disease locally (respectively, choose an economic optimum resulting in not to wipe out the disease completely or take no vaccination for anyone) provided the vaccine failure rate is relatively small (respectively, intermediate or large). Numerical simulations to illustrate our main results are also provided. Moreover, the data collected at the height of the Covid-19 pandemic in Taiwan are also numerically simulated to provide the corresponding optimal vaccination strategy.
Collapse
Affiliation(s)
- Yu-Jhe Huang
- Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan
| | - An-Tien Hsiao
- Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan
| | - Jonq Juang
- Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan
| |
Collapse
|
38
|
Wei X, Zhao J, Liu S, Wang Y. Identifying influential spreaders in complex networks for disease spread and control. Sci Rep 2022; 12:5550. [PMID: 35365715 PMCID: PMC8973685 DOI: 10.1038/s41598-022-09341-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2021] [Accepted: 02/23/2022] [Indexed: 11/09/2022] Open
Abstract
Identifying influential spreaders is an important task in controlling the spread of information and epidemic diseases in complex networks. Many recent studies have indicated that the identification of influential spreaders is dependent on the spreading dynamics. Finding a general optimal order of node importance ranking is difficult because of the complexity of network structures and the physical background of dynamics. In this paper, we use four metrics, namely, betweenness, degree, H-index, and coreness, to measure the central attributes of nodes for constructing the disease spreading models and target immunization strategies. Numerical simulations show that spreading processes based on betweenness centrality lead to the widest range of propagation and the smallest epidemic threshold for all six networks (including four real networks and two BA scale-free networks generated according to Barabasi–Albert algorithm). The target immunization strategy based on the betweenness centrality of nodes is the most effective for BA scale-free networks but displays poor immune effect for real networks in identifying the most important spreaders for disease control. The immunization strategy based on node degrees is the most effective for the four real networks. Findings show that the target immune strategy based on the betweenness centrality of nodes works best for standard scale-free networks, whereas that based on node degrees works best for other nonstandard scale-free networks. The results can provide insights into understanding the different metrics of measuring node importance in disease transmission and control.
Collapse
Affiliation(s)
- Xiang Wei
- Department of Engineering, Honghe University, Honghe, 661100, People's Republic of China.
| | - Junchan Zhao
- School of Science, Hunan University of Technology and Business, Changsha, 410205, People's Republic of China
| | - Shuai Liu
- Department of Engineering, Honghe University, Honghe, 661100, People's Republic of China
| | - Yisi Wang
- School of Big Data Science and Application, Chongqing Wenli University, Chongqing, 402160, People's Republic of China
| |
Collapse
|
39
|
Nakamura GM, Souza ACC, Souza FCM, Bulcao-Neto RF, Martinez AS, Macedo AA. Using Symmetry to Enhance the Performance of Agent-Based Epidemic Models. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2022; 19:1245-1254. [PMID: 32833641 DOI: 10.1109/tcbb.2020.3018901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Symmetries express the invariance of a system towards sets of mathematical transformations. In more practical terms, symmetries greatly reduce or simplify the computational efforts required to evaluate relevant properties of a system. In this paper, two methods are proposed to implement spin symmetries which simplify the analysis of the spreading of diseases in an agent-based epidemic model. We perform a set of simulations to measure the efficiency gains compared to traditional methods. Our findings show symmetry-based algorithms improve the performance of the Monte Carlo simulation and the exact Markov process.
Collapse
|
40
|
Huang Y, Zhu Q. Game-Theoretic Frameworks for Epidemic Spreading and Human Decision-Making: A Review. DYNAMIC GAMES AND APPLICATIONS 2022; 12:7-48. [PMID: 35194521 PMCID: PMC8853398 DOI: 10.1007/s13235-022-00428-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 01/02/2022] [Indexed: 05/28/2023]
Abstract
This review presents and reviews various solved and open problems in developing, analyzing, and mitigating epidemic spreading processes under human decision-making. We provide a review of a range of epidemic models and explain the pros and cons of different epidemic models. We exhibit the art of coupling between epidemic models and decision models in the existing literature. More specifically, we provide answers to fundamental questions in human decision-making amid epidemics, including what interventions to take to combat the disease, who are decision-makers, and when and how to take interventions, and how to make interventions. Among many decision models, game-theoretic models have become increasingly crucial in modeling human responses or behavior amid epidemics in the last decade. In this review, we motivate the game-theoretic approach to human decision-making amid epidemics. This review provides an overview of the existing literature by developing a multi-dimensional taxonomy, which categorizes existing literature based on multiple dimensions, including (1) types of games, such as differential games, stochastic games, evolutionary games, and static games; (2) types of interventions, such as social distancing, vaccination, quarantine, and taking antidotes; (3) the types of decision-makers, such as individuals, adversaries, and central authorities at different hierarchical levels. A fine-grained dynamic game framework is proposed to capture the essence of game-theoretic decision-making amid epidemics. We showcase three representative frameworks with unique ways of integrating game-theoretic decision-making into the epidemic models from a vast body of literature. Each of the three frameworks has their unique way of modeling and analyzing and develops results from different angles. In the end, we identify several main open problems and research gaps left to be addressed and filled.
Collapse
Affiliation(s)
- Yunhan Huang
- New York University, 370 Jay Street, Brooklyn, NY USA
| | - Quanyan Zhu
- New York University, 370 Jay Street, Brooklyn, NY USA
| |
Collapse
|
41
|
Gomes MGM, Ferreira MU, Corder RM, King JG, Souto-Maior C, Penha-Gonçalves C, Gonçalves G, Chikina M, Pegden W, Aguas R. Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold. MEDRXIV : THE PREPRINT SERVER FOR HEALTH SCIENCES 2022:2020.04.27.20081893. [PMID: 32511451 PMCID: PMC7239079 DOI: 10.1101/2020.04.27.20081893] [Citation(s) in RCA: 128] [Impact Index Per Article: 64.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Individual variation in susceptibility and exposure is subject to selection by natural infection, accelerating the acquisition of immunity, and reducing herd immunity thresholds and epidemic final sizes. This is a manifestation of a wider population phenomenon known as "frailty variation". Despite theoretical understanding, public health policies continue to be guided by mathematical models that leave out considerable variation and as a result inflate projected disease burdens and overestimate the impact of interventions. Here we focus on trajectories of the coronavirus disease (COVID-19) pandemic in England and Scotland until November 2021. We fit models to series of daily deaths and infer relevant epidemiological parameters, including coefficients of variation and effects of non-pharmaceutical interventions which we find in agreement with independent empirical estimates based on contact surveys. Our estimates are robust to whether the analysed data series encompass one or two pandemic waves and enable projections compatible with subsequent dynamics. We conclude that vaccination programmes may have contributed modestly to the acquisition of herd immunity in populations with high levels of pre-existing naturally acquired immunity, while being critical to protect vulnerable individuals from severe outcomes as the virus becomes endemic.
Collapse
Affiliation(s)
- M Gabriela M Gomes
- Department of Mathematics and Statistics, University of Strathclyde, Glasgow, UK
- Centro de Matemática e Aplicações, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal
| | - Marcelo U Ferreira
- Institute of Biomedical Sciences, University of São Paulo, São Paulo, Brazil
- Global Health and Tropical Medicine, Institute of Hygiene and Tropical Medicine, Nova University of Lisbon, Lisbon, Portugal
| | - Rodrigo M Corder
- Institute of Biomedical Sciences, University of São Paulo, São Paulo, Brazil
| | - Jessica G King
- Institute of Evolutionary Biology, University of Edinburgh, Edinburgh, UK
| | - Caetano Souto-Maior
- Laboratory of Systems Genetics, National Heart Lung and Blood Institute, National Institutes of Health, Bethesda, MD, USA
| | | | - Guilherme Gonçalves
- Unidade Multidisciplinar de Investigação Biomédica, Instituto de Ciências Biomédicas Abel Salazar, Universidade do Porto, Porto, Portugal
| | - Maria Chikina
- Department of Computational and Systems Biology, University of Pittsburgh, Pittburgh, PA, USA
| | - Wesley Pegden
- Department of Mathematical Sciences, Carnegie Mellon University, , Pittburgh" , PA, USA
| | - Ricardo Aguas
- Centre for Tropical Medicine and Global Health, Nuffield Department of Medicine, University of Oxford, Oxford, UK
| |
Collapse
|
42
|
Ortega E, Machado D, Lage-Castellanos A. Dynamics of epidemics from cavity master equations: Susceptible-infectious-susceptible models. Phys Rev E 2022; 105:024308. [PMID: 35291082 DOI: 10.1103/physreve.105.024308] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2021] [Accepted: 01/27/2022] [Indexed: 05/23/2023]
Abstract
We apply the recently introduced cavity master equation (CME) to epidemic models and compare it to previously known approaches. We show that CME seems to be the formal way to derive (and correct) dynamic message passing (rDMP) equations that were previously introduced in an intuitive ad hoc manner. CME outperforms rDMP in all cases studied. Both approximations are nonbacktracking and this causes CME and rDMP to fail when the ecochamber mechanism is relevant, as in loopless topologies or scale free networks. However, we studied several random regular graphs and Erdős-Rényi graphs, where CME outperforms individual based mean field and a type of pair based mean field, although it is less precise than pair quenched mean field. We derive analytical results for endemic thresholds and compare them across different approximations.
Collapse
Affiliation(s)
- Ernesto Ortega
- Complex Systems Group, Physics Faculty, Havana University, 10400 Havana, Cuba
| | - David Machado
- Complex Systems Group, Physics Faculty, Havana University, 10400 Havana, Cuba
| | | |
Collapse
|
43
|
Bestehorn M, Michelitsch TM, Collet BA, Riascos AP, Nowakowski AF. Simple model of epidemic dynamics with memory effects. Phys Rev E 2022; 105:024205. [PMID: 35291108 DOI: 10.1103/physreve.105.024205] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2021] [Accepted: 02/08/2022] [Indexed: 06/14/2023]
Abstract
We introduce a compartment model with memory for the dynamics of epidemic spreading in a constant population of individuals. Each individual is in one of the states S=susceptible, I=infected, or R=recovered (SIR model). In state R an individual is assumed to stay immune within a finite-time interval. In the first part, we introduce a random lifetime or duration of immunity which is drawn from a certain probability density function. Once the time of immunity is elapsed an individual makes an instantaneous transition to the susceptible state. By introducing a random duration of immunity a memory effect is introduced into the process which crucially determines the epidemic dynamics. In the second part, we investigate the influence of the memory effect on the space-time dynamics of the epidemic spreading by implementing this approach into computer simulations and employ a multiple random walker's model. If a susceptible walker meets an infectious one on the same site, then the susceptible one gets infected with a certain probability. The computer experiments allow us to identify relevant parameters for spread or extinction of an epidemic. In both parts, the finite duration of immunity causes persistent oscillations in the number of infected individuals with ongoing epidemic activity preventing the system from relaxation to a steady state solution. Such oscillatory behavior is supported by real-life observations and not captured by the classical standard SIR model.
Collapse
Affiliation(s)
- Michael Bestehorn
- Brandenburgische Technische Universität Cottbus-Senftenberg, Institut für Physik, Erich-Weinert-Straße 1, 03046 Cottbus, Germany
| | - Thomas M Michelitsch
- Sorbonne Université, Institut Jean le Rond d'Alembert, CNRS UMR 7190, 4 place Jussieu, 75252 Paris cedex 05, France
| | - Bernard A Collet
- Sorbonne Université, Institut Jean le Rond d'Alembert, CNRS UMR 7190, 4 place Jussieu, 75252 Paris cedex 05, France
| | - Alejandro P Riascos
- Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 Ciudad de México, México
| | - Andrzej F Nowakowski
- Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, United Kingdom
| |
Collapse
|
44
|
Xie B, Liu M, Zhang L. Bifurcation analysis and optimal control of SEIR epidemic model with saturated treatment function on the network. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:1677-1696. [PMID: 35135224 DOI: 10.3934/mbe.2022079] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
In order to study the impact of limited medical resources and population heterogeneity on disease transmission, a SEIR model based on a complex network with saturation processing function is proposed. This paper first proved that a backward bifurcation occurs under certain conditions, which means that R0<1 is not enough to eradicate this disease from the population. However, if the direction is positive, we find that within a certain parameter range, there may be multiple equilibrium points near R0=1. Secondly, the influence of population heterogeneity on virus transmission is analyzed, and the optimal control theory is used to further study the time-varying control of the disease. Finally, numerical simulations verify the stability of the system and the effectiveness of the optimal control strategy.
Collapse
Affiliation(s)
- Boli Xie
- School of Science, North University of China, Taiyuan 030051, China
| | - Maoxing Liu
- School of Science, North University of China, Taiyuan 030051, China
| | - Lei Zhang
- School of Science, North University of China, Taiyuan 030051, China
| |
Collapse
|
45
|
Baumgarten L, Bornholdt S. Epidemics with asymptomatic transmission: Subcritical phase from recursive contact tracing. Phys Rev E 2021; 104:054310. [PMID: 34942758 DOI: 10.1103/physreve.104.054310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2020] [Accepted: 11/16/2021] [Indexed: 11/07/2022]
Abstract
The challenges presented by the COVID-19 epidemic have created a renewed interest in the development of new methods to combat infectious diseases, and it has shown the importance of preparedness for possible future diseases. A prominent property of the SARS-CoV-2 transmission is the significant fraction of asymptomatic transmission. This may influence the effectiveness of the standard contact tracing procedure for quarantining potentially infected individuals. However, the effects of asymptomatic transmission on the epidemic threshold of epidemic spreading on networks have rarely been studied explicitly. Here we study the critical percolation transition for an arbitrary disease with a nonzero asymptomatic rate in a simple epidemic network model in the presence of a recursive contact tracing algorithm for instant quarantining. We find that, above a certain fraction of asymptomatic transmission, standard contact tracing loses its ability to suppress spreading below the epidemic threshold. However, we also find that recursive contact tracing opens a possibility to contain epidemics with a large fraction of asymptomatic or presymptomatic transmission. In particular, we calculate the required fraction of network nodes participating in the contact tracing for networks with arbitrary degree distributions and for varying recursion depths and discuss the influence of recursion depth and asymptomatic rate on the epidemic percolation phase transition. We anticipate recursive contact tracing to provide a basis for digital, app-based contact tracing tools that extend the efficiency of contact tracing to diseases with a large fraction of asymptomatic transmission.
Collapse
Affiliation(s)
- Lorenz Baumgarten
- Institut für Theoretische Physik, Universität Bremen, 28759 Bremen, Germany
| | - Stefan Bornholdt
- Institut für Theoretische Physik, Universität Bremen, 28759 Bremen, Germany
| |
Collapse
|
46
|
Harper R, Tee P. Balancing capacity and epidemic spread in the global airline network. APPLIED NETWORK SCIENCE 2021; 6:94. [PMID: 34849399 PMCID: PMC8613734 DOI: 10.1007/s41109-021-00432-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/02/2021] [Accepted: 10/06/2021] [Indexed: 06/13/2023]
Abstract
The structure of complex networks has long been understood to play a role in transmission and spreading phenomena on a graph. Such networks form an important part of the structure of society, including transportation networks. As society fights to control the COVID-19 pandemic, an important question is how to choose the optimum balance between the full opening of transport networks and the control of epidemic spread. In this work we investigate the interplay between network dismantling and epidemic spread rate as a proxy for the imposition of travel restrictions to control disease spread. For network dismantling we focus on the weighted and unweighted forms of metrics that capture the topological and informational structure of the network. Our results indicate that there is benefit to a directed approach to imposing travel restrictions, but we identify that more detailed models of the transport network are necessary for definitive results.
Collapse
Affiliation(s)
| | - Philip Tee
- Science Group, Moogsoft Inc., San Francisco, CA USA
- The Beyond Center for Fundamental Science, University of Arizona, Tempe, AZ USA
- Department of Informatics, University of Sussex, Falmer, Brighton, UK
| |
Collapse
|
47
|
Tkachenko AV, Maslov S, Wang T, Elbana A, Wong GN, Goldenfeld N. Stochastic social behavior coupled to COVID-19 dynamics leads to waves, plateaus, and an endemic state. eLife 2021; 10:68341. [PMID: 34747698 PMCID: PMC8670744 DOI: 10.7554/elife.68341] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2021] [Accepted: 11/04/2021] [Indexed: 12/23/2022] Open
Abstract
It is well recognized that population heterogeneity plays an important role in the spread of epidemics. While individual variations in social activity are often assumed to be persistent, that is, constant in time, here we discuss the consequences of dynamic heterogeneity. By integrating the stochastic dynamics of social activity into traditional epidemiological models, we demonstrate the emergence of a new long timescale governing the epidemic, in broad agreement with empirical data. Our stochastic social activity model captures multiple features of real-life epidemics such as COVID-19, including prolonged plateaus and multiple waves, which are transiently suppressed due to the dynamic nature of social activity. The existence of a long timescale due to the interplay between epidemic and social dynamics provides a unifying picture of how a fast-paced epidemic typically will transition to an endemic state.
Collapse
Affiliation(s)
- Alexei V Tkachenko
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, United States
| | - Sergei Maslov
- Department of Bioengineering, University of Illinois Urbana-Champaign, Urbana, United States
| | - Tong Wang
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, United States
| | - Ahmed Elbana
- Department of Civil Engineering, University of Illinois at Urbana-Champaign, Urbana, United States
| | - George N Wong
- Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, United States
| | - Nigel Goldenfeld
- University of Illinois at Urbana-Champaign, Urbana, United States
| |
Collapse
|
48
|
Zhang S, Yang H. Spatial Modeling and Analysis of Human Traffic and Infectious Virus Spread in Community Networks. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2021; 2021:2286-2289. [PMID: 34891743 DOI: 10.1109/embc46164.2021.9630798] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The use of network models to study the spread of infectious diseases is gaining increasing interests. They allow the flexibility to represent epidemic systems as networks of components with complex and interconnected structures. However, most of previous studies are based on networks of individuals as nodes and their social relationships (e.g., friendship, workplace connections) as links during the virus spread process. Notably, the transmission and spread of infectious viruses are more pertinent to human dynamics (e.g., their movements and interactions with others) in the spatial environment. This paper presents a novel network-based simulation model of human traffic and virus spread in community networks. We represent spatial points of interests (POI) as nodes where human subjects interact and perform activities, while edges connect these POIs to form a community network. Specifically, we derive the spatial network from the geographical information systems (GIS) data to provide a detailed representation of the underlying community network, on which human subjects perform activities and form traffics that impact the process of virus transmission and spread. The proposed framework is evaluated and validated in a community of university campus. Experimental results showed that the proposed simulation model is capable of describing interactive human activities at an individual level, as well as capturing the spread dynamics of infectious diseases. This framework can be extended to a wide variety of infectious diseases and shows strong potentials to aid the design of intervention policies for epidemic control.
Collapse
|
49
|
A stochastic model explains the periodicity phenomenon of influenza on network. Sci Rep 2021; 11:20996. [PMID: 34697349 PMCID: PMC8546073 DOI: 10.1038/s41598-021-00260-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2021] [Accepted: 09/24/2021] [Indexed: 11/08/2022] Open
Abstract
Influenza is an infectious disease with obvious periodic changes over time. It is of great practical significance to explore the non-environment-related factors that cause this regularity for influenza control and individual protection. In this paper, based on the randomness of population number and the heterogeneity of population contact, we have established a stochastic infectious disease model about influenza based on the degree of the network, and obtained the power spectral density function by using the van Kampen expansion method of the master equation. The relevant parameters are obtained by fitting the influenza data of sentinel hospitals. The results of the numerical analysis show that: (1) for the infected, the infection period of patients who go to the sentinel hospitals is particularly different from the others who do not; (2) for all the infected, there is an obvious nonlinear relationship between their infection period and the visiting rate of the influenza sentinel hospitals, the infection rate and the degree. Among them, only the infection period of patients who do not go to the sentinel hospitals decreased monotonously with the infection rate (increased monotonously with the visiting rate), while the rest had a non-monotonic relationship.
Collapse
|
50
|
Lu Z, Wahlström J, Nehorai A. Containing epidemics in a local cluster via antidote distribution and partial quarantine. Phys Rev E 2021; 104:034307. [PMID: 34654168 DOI: 10.1103/physreve.104.034307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2021] [Accepted: 08/26/2021] [Indexed: 11/07/2022]
Abstract
The study of spreading phenomena in networks, in particular the spread of disease, has attracted considerable interest in the network science research community. In this paper, we show that the outbreak of an epidemic can be effectively contained and suppressed in a small subnetwork by a combination of antidote distribution and partial quarantine. We improve over existing antidote distribution schemes based on personalized PageRank in two ways. First, we replace the constraint on the topology of this subnetwork described by Chung et al. [Internet Math. 6, 237 (2009)1542-795110.1080/15427951.2009.10129184] that a large fraction of the value of the personalized PageRank vector must be contained in the local cluster, with a partial quarantine scheme. Second, we derive a different lower bound on the amount of antidote. We show that, under our antidote distribution scheme, the probability of the infection spreading to the whole network is bounded, and the infection inside the subnetwork will disappear after a period that is proportional to the logarithm of the number of initially infected nodes. We demonstrate the effectiveness of our strategy with numerical simulations of epidemics on benchmark networks. We also test our strategy on two examples of epidemics in real-world networks. Our strategy is dependent only on the rate of infection, the rate of recovery, and the topology around the initially infected nodes, and is independent of the rest of the network.
Collapse
Affiliation(s)
- Zhenqi Lu
- Preston M. Green Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | - Johan Wahlström
- Department of Computer Science, University of Exeter, Exeter EX4 4QF, United Kingdom
| | - Arye Nehorai
- Preston M. Green Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| |
Collapse
|