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Liu X, Hu Q, Wang J, Wu X, Hu D. Difference in Rumor Dissemination and Debunking Before and After the Relaxation of COVID-19 Prevention and Control Measures in China: Infodemiology Study. J Med Internet Res 2024; 26:e48564. [PMID: 38748460 PMCID: PMC11137433 DOI: 10.2196/48564] [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: 04/28/2023] [Revised: 01/11/2024] [Accepted: 04/11/2024] [Indexed: 06/01/2024] Open
Abstract
BACKGROUND The information epidemic emerged along with the COVID-19 pandemic. While controlling the spread of COVID-19, the secondary harm of epidemic rumors to social order cannot be ignored. OBJECTIVE The objective of this paper was to understand the characteristics of rumor dissemination before and after the pandemic and the corresponding rumor management and debunking mechanisms. This study aimed to provide a theoretical basis and effective methods for relevant departments to establish a sound mechanism for managing network rumors related to public health emergencies such as COVID-19. METHODS This study collected data sets of epidemic rumors before and after the relaxation of the epidemic prevention and control measures, focusing on large-scale network rumors. Starting from 3 dimensions of rumor content construction, rumor propagation, and rumor-refuting response, the epidemic rumors were subdivided into 7 categories, namely, involved subjects, communication content, emotional expression, communication channels, communication forms, rumor-refuting subjects, and verification sources. Based on this framework, content coding and statistical analysis of epidemic rumors were carried out. RESULTS The study found that the rumor information was primarily directed at a clear target audience. The main themes of rumor dissemination were related to the public's immediate interests in the COVID-19 field, with significant differences in emotional expression and mostly negative emotions. Rumors mostly spread through social media interactions, community dissemination, and circle dissemination, with text content as the main form, but they lack factual evidence. The preferences of debunking subjects showed differences, and the frequent occurrence of rumors reflected the unsmooth channels of debunking. The χ2 test of data before and after the pandemic showed that the P value was less than .05, indicating that the difference in rumor content before and after the pandemic had statistical significance. CONCLUSIONS This study's results showed that the themes of rumors during the pandemic are closely related to the immediate interests of the public, and the emotions of the public accelerate the spread of these rumors, which are mostly disseminated through social networks. Therefore, to more effectively prevent and control the spread of rumors during the pandemic and to enhance the capability to respond to public health crises, relevant authorities should strengthen communication with the public, conduct emotional risk assessments, and establish a joint mechanism for debunking rumors.
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Affiliation(s)
- Xiaoqi Liu
- Department of Biomedical Informatics, School of Life Sciences, Central South University, Changsha, Hunan, China
| | - Qingyuan Hu
- Department of Research, The Third Xiangya Hospital of Central South University, Changsha, Hunan, China
| | - Jie Wang
- School of Life Sciences, Central South University, Changsha, Hunan, China
| | - Xusheng Wu
- Shenzhen Health Care Development Research and Data Management Center, Shenzhen, Guangdong, China
| | - Dehua Hu
- Department of Biomedical Informatics, School of Life Sciences, Central South University, Changsha, Hunan, China
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2
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Gao W, Wang Y, Cao J, Liu Y. Final epidemic size and critical times for susceptible-infectious-recovered models with a generalized contact rate. CHAOS (WOODBURY, N.Y.) 2024; 34:013152. [PMID: 38294886 DOI: 10.1063/5.0185707] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2023] [Accepted: 12/27/2023] [Indexed: 02/02/2024]
Abstract
During the spread of an infectious disease, the contact rate or the incidence rate may affect disease characteristics. For simplicity, most disease models assume standard incidence or mass action rates to calculate the basic reproduction number, final epidemic size, and peak time of an epidemic. For standard incidence, the contact rate remains constant resulting in the incidence rate is inversely proportional to the population size, while for the mass action rate, this contact rate is proportional to the total population size resulting in the incidence rate is independent of the population size. In this paper, we consider susceptible-infectious-recovered epidemic models with a generalized contact rate C(N) and a nonlinear incidence rate in view of the behavioral change from susceptible or infectious individuals when an infectious disease appears. The basic reproduction number and the final size equation are derived. The impact of different types of contact rates on them is studied. Moreover, two critical times (peak time and epidemic duration) of an epidemic are considered. Explicit formulas for the peak time and epidemic duration are obtained. These formulas are helpful not only for taking early effective epidemic precautions but also for understanding how the epidemic duration can be changed by acting on the model parameters, especially when the epidemic model is used to make public health policy.
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Affiliation(s)
- Wenhua Gao
- School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China
| | - Yi Wang
- School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China
- School of Mathematics, Southeast University, Nanjing 210096, China
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 210096, China
| | - Yang Liu
- Laboratory of Intelligent Education Technology and Application of Zhejiang Province, School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China
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Savi MK, Yadav A, Zhang W, Vembar N, Schroeder A, Balsari S, Buckee CO, Vadhan S, Kishore N. A standardised differential privacy framework for epidemiological modeling with mobile phone data. PLOS DIGITAL HEALTH 2023; 2:e0000233. [PMID: 37889905 PMCID: PMC10610440 DOI: 10.1371/journal.pdig.0000233] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2023] [Accepted: 09/03/2023] [Indexed: 10/29/2023]
Abstract
During the COVID-19 pandemic, the use of mobile phone data for monitoring human mobility patterns has become increasingly common, both to study the impact of travel restrictions on population movement and epidemiological modeling. Despite the importance of these data, the use of location information to guide public policy can raise issues of privacy and ethical use. Studies have shown that simple aggregation does not protect the privacy of an individual, and there are no universal standards for aggregation that guarantee anonymity. Newer methods, such as differential privacy, can provide statistically verifiable protection against identifiability but have been largely untested as inputs for compartment models used in infectious disease epidemiology. Our study examines the application of differential privacy as an anonymisation tool in epidemiological models, studying the impact of adding quantifiable statistical noise to mobile phone-based location data on the bias of ten common epidemiological metrics. We find that many epidemiological metrics are preserved and remain close to their non-private values when the true noise state is less than 20, in a count transition matrix, which corresponds to a privacy-less parameter ϵ = 0.05 per release. We show that differential privacy offers a robust approach to preserving individual privacy in mobility data while providing useful population-level insights for public health. Importantly, we have built a modular software pipeline to facilitate the replication and expansion of our framework.
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Affiliation(s)
- Merveille Koissi Savi
- Department of Medical Oncology, Dana Farber Cancer Institute, Harvard School of Medicine, Boston, Massachusetts, United States of America
| | - Akash Yadav
- Direct Relief, Santa Barbara, California, United States of America
| | - Wanrong Zhang
- Department of Computer Sciences, Harvard John A. Paulson School of Engineering & Applied Sciences, Boston, Massachusetts, United States of America
| | - Navin Vembar
- Camber Systems, Washington, District of Columbia, United States of America
| | - Andrew Schroeder
- Direct Relief, Santa Barbara, California, United States of America
| | - Satchit Balsari
- Department of Emergency Medicine, Harvard Medical School, Boston, Massachusetts, United States of America
| | - Caroline O. Buckee
- Department of Epidemiology, Harvard TH Chan School of Public Health, Boston, Massachusetts, United States of America
| | - Salil Vadhan
- Department of Computer Sciences, Harvard John A. Paulson School of Engineering & Applied Sciences, Boston, Massachusetts, United States of America
| | - Nishant Kishore
- Department of Epidemiology, Harvard TH Chan School of Public Health, Boston, Massachusetts, United States of America
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4
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Demers J, Fagan WF, Potluri S, Calabrese JM. The relationship between controllability, optimal testing resource allocation, and incubation-latent period mismatch as revealed by COVID-19. Infect Dis Model 2023; 8:514-538. [PMID: 37250860 PMCID: PMC10186984 DOI: 10.1016/j.idm.2023.04.007] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2023] [Revised: 04/21/2023] [Accepted: 04/25/2023] [Indexed: 05/31/2023] Open
Abstract
The severe shortfall in testing supplies during the initial COVID-19 outbreak and ensuing struggle to manage the pandemic have affirmed the critical importance of optimal supply-constrained resource allocation strategies for controlling novel disease epidemics. To address the challenge of constrained resource optimization for managing diseases with complications like pre- and asymptomatic transmission, we develop an integro partial differential equation compartmental disease model which incorporates realistic latent, incubation, and infectious period distributions along with limited testing supplies for identifying and quarantining infected individuals. Our model overcomes the limitations of typical ordinary differential equation compartmental models by decoupling symptom status from model compartments to allow a more realistic representation of symptom onset and presymptomatic transmission. To analyze the influence of these realistic features on disease controllability, we find optimal strategies for reducing total infection sizes that allocate limited testing resources between 'clinical' testing, which targets symptomatic individuals, and 'non-clinical' testing, which targets non-symptomatic individuals. We apply our model not only to the original, delta, and omicron COVID-19 variants, but also to generically parameterized disease systems with varying mismatches between latent and incubation period distributions, which permit varying degrees of presymptomatic transmission or symptom onset before infectiousness. We find that factors that decrease controllability generally call for reduced levels of non-clinical testing in optimal strategies, while the relationship between incubation-latent mismatch, controllability, and optimal strategies is complicated. In particular, though greater degrees of presymptomatic transmission reduce disease controllability, they may increase or decrease the role of non-clinical testing in optimal strategies depending on other disease factors like transmissibility and latent period length. Importantly, our model allows a spectrum of diseases to be compared within a consistent framework such that lessons learned from COVID-19 can be transferred to resource constrained scenarios in future emerging epidemics and analyzed for optimality.
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Affiliation(s)
- Jeffery Demers
- Center for Advanced Systems Understanding (CASUS), Helmholtz-Zentrum Dresden-Rosendorf (HZDR), Görlitz, Germany
- Dept. of Biology, University of Maryland, College Park, MD, USA
| | - William F Fagan
- Dept. of Biology, University of Maryland, College Park, MD, USA
| | - Sriya Potluri
- Dept. of Biology, University of Maryland, College Park, MD, USA
| | - Justin M Calabrese
- Center for Advanced Systems Understanding (CASUS), Helmholtz-Zentrum Dresden-Rosendorf (HZDR), Görlitz, Germany
- Dept. of Biology, University of Maryland, College Park, MD, USA
- Dept. of Ecological Modelling, Helmholtz Centre for Environmental Research-UFZ, Leipzig, Germany
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5
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Samadder S, Ghosh K. The changing economic relationship between some of the major COVID-19 impacted countries with prominent wealth: a comparative study from the view point of stock markets. THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS 2022; 231:3505-3535. [PMID: 35789684 PMCID: PMC9244491 DOI: 10.1140/epjs/s11734-022-00616-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/12/2021] [Accepted: 05/25/2022] [Indexed: 06/15/2023]
Abstract
In the present work, a study has been made over the prime stock indices of some fiscally prominent countries impacted by COVID-19. The countries are separated in two ways: (1) considering gross total number of infected cases-here seven mostly impacted countries with certain global economic influence are selected; (2) considering the concentration of the infected cases-here six major impacted countries with considerable influence are selected. This sort of categorization is itself a novel strategy which is capable of including some less populated, but severely impacted countries of economic importance. The objective of the present analysis is to comprehend the impact of COVID-19 on these markets and to recognize the effect of COVID-19 on mutual association and dependence between these markets. To add more flavour of reliability, we have taken a new and fresh strategy of fixing the time frames under consideration before and during COVID-19 pandemic as uniform. We have used both linear and nonlinear Granger causality analysis and employed generalized forecast error variance decomposition analysis to review the exogeneity and endogeneity of the individual markets. The present study shows that this pandemic has changed the underlying relationship: some exogenous stock markets have become endogenous and vice versa in the pandemic. Linear relationship has been reduced radically, whereas nonlinear relationship has been improved during the COVID-affected period. TASE, the highest returned and significantly uncorrelated index, emerged as the most exogenous market in the pre-COVID period, though it is nonlinearly endogenous in the long term, in the COVD-affected period. CAC 40 is the most endogenous market for the short term in both pre-COVID and COVID-affected period. B3 and NYSE, exogenous in the pre-COVID period, turned out to be linearly endogenous in the COVID-affected duration, whereas BIST 100 and BSE SENSEX are found to be exogenous markets in the COVID-affected period according to both linear and nonlinear causal analysis. They were also exogenous in the pre-COVID era for the short-term period, with BSE SENSEX exhibiting exogeneity anti-persistently for the COVID-affected period too. Association among the markets is more in long term rather than short term. A possible conclusion is also that the markets may regain long-term association once the effect of COVID would fade away.
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Affiliation(s)
- Swetadri Samadder
- Department of Mathematics, Fakir Chand College, South 24 Parganas, Diamond Harbour, 743331 India
| | - Koushik Ghosh
- Department of Mathematics, University Institute of Technology, The University of Burdwan, Golapbag (North), Burdwan, 713104 India
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6
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Dynamic Analysis of a COVID-19 Vaccination Model with a Positive Feedback Mechanism and Time-Delay. MATHEMATICS 2022. [DOI: 10.3390/math10091583] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
As the novel coronavirus pandemic has spread globally since 2019, most countries in the world are conducting vaccination campaigns. First, based on the traditional SIR infectious disease model, we introduce a positive feedback mechanism associated with the vaccination rate, and consider the time delay from antibody production to antibody disappearance after vaccination. We establish an UVaV model for COVID-19 vaccination with a positive feedback mechanism and time-delay. Next, we verify the existence of the equilibrium of the formulated model and analyze its stability. Then, we analyze the existence of the Hopf bifurcation, and use the multiple time scales method to derive the normal form of the Hopf bifurcation, further determining the direction of the Hopf bifurcation and the stability of the periodic solution of the bifurcation. Finally, we collect the parameter data of some countries and regions to determine the reasonable ranges of multiple parameters to ensure the authenticity of simulation results. Numerical simulations are carried out to verify the correctness of the theoretical results. We also give the critical time for controllable widespread antibody failure to provide a reference for strengthening vaccination time. Taking two groups of parameters as examples, the time of COVID-19 vaccine booster injection should be best controlled before 38.5 weeks and 35.3 weeks, respectively. In addition, study the impact of different expiration times on epidemic prevention and control effectiveness. We further explore the impact of changes in vaccination strategies on trends in epidemic prevention and control effectiveness. It could be concluded that, under the same epidemic vaccination strategy, the existence level of antibody is roughly the same, which is consistent with the reality.
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7
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James N, Menzies M, Bondell H. Comparing the dynamics of COVID-19 infection and mortality in the United States, India, and Brazil. PHYSICA D. NONLINEAR PHENOMENA 2022; 432:133158. [PMID: 35075315 PMCID: PMC8769590 DOI: 10.1016/j.physd.2022.133158] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2021] [Revised: 12/06/2021] [Accepted: 01/08/2022] [Indexed: 05/07/2023]
Abstract
This paper compares and contrasts the spread and impact of COVID-19 in the three countries most heavily impacted by the pandemic: the United States (US), India and Brazil. All three of these countries have a federal structure, in which the individual states have largely determined the response to the pandemic. Thus, we perform an extensive analysis of the individual states of these three countries to determine patterns of similarity within each. First, we analyse structural similarity and anomalies in the trajectories of cases and deaths as multivariate time series. Next, we study the lengths of the different waves of the virus outbreaks across the three countries and their states. Finally, we investigate suitable time offsets between cases and deaths as a function of the distinct outbreak waves. In all these analyses, we consistently reveal more characteristically distinct behaviour between US and Indian states, while Brazilian states exhibit less structure in their wave behaviour and changing progression between cases and deaths.
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Affiliation(s)
- Nick James
- School of Mathematics and Statistics, University of Melbourne, Victoria, Australia
| | - Max Menzies
- Beijing Institute of Mathematical Sciences and Applications, Tsinghua University, Beijing, China
| | - Howard Bondell
- School of Mathematics and Statistics, University of Melbourne, Victoria, Australia
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8
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Cremonini M, Maghool S. The dynamical formation of ephemeral groups on networks and their effects on epidemics spreading. Sci Rep 2022; 12:683. [PMID: 35027604 PMCID: PMC8758734 DOI: 10.1038/s41598-021-04589-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2021] [Accepted: 12/21/2021] [Indexed: 12/24/2022] Open
Abstract
In network models of propagation processes, the individual, microscopic level perspective is the norm, with aggregations studied as possible outcomes. On the contrary, we adopted a mesoscale perspective with groups as the core element and in this sense we present a novel agent-group dynamic model of propagation in networks. In particular, we focus on ephemeral groups that dynamically form, create new links, and dissolve. The experiments simulated 160 model configurations and produced results describing cases of consecutive and non-consecutive dynamic grouping, bounded or unbounded in the number of repetitions. Results revealed the existence of complex dynamics and multiple behaviors. An efficiency metric is introduced to compare the different cases. A Null Model analysis disclosed a pattern in the difference between the group and random models, varying with the size of groups. Our findings indicate that a mesoscopic construct like the ephemeral group, based on assumptions about social behavior and absent any microscopic level change, could produce and describe complex propagation dynamics. A conclusion is that agent-group dynamic models may represent a powerful approach for modelers and a promising new direction for future research in models of coevolution between propagation and behavior in society.
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Affiliation(s)
- Marco Cremonini
- Department of Political and Social Sciences, University of Milan, Milan, Italy.
| | - Samira Maghool
- Department of Computer Science, University of Milan, Milan, Italy.
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9
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James N, Menzies M. Estimating a continuously varying offset between multivariate time series with application to COVID-19 in the United States. THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS 2022; 231:3419-3426. [PMID: 35035778 PMCID: PMC8749119 DOI: 10.1140/epjs/s11734-022-00430-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2021] [Accepted: 12/18/2021] [Indexed: 05/04/2023]
Abstract
This paper introduces new methods to track the offset between two multivariate time series on a continuous basis. We then apply this framework to COVID-19 counts on a state-by-state basis in the United States to determine the progression from cases to deaths as a function of time. Across multiple approaches, we reveal an "up-down-up" pattern in the estimated offset between reported cases and deaths as the pandemic progresses. This analysis could be used to predict imminent increased load on a healthcare system and aid the allocation of additional resources in advance.
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Affiliation(s)
- Nick James
- School of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010 Australia
| | - Max Menzies
- Beijing Institute of Mathematical Sciences and Applications, Tsinghua University, Beijing, 101408 China
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10
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James N, Menzies M. Trends in COVID-19 prevalence and mortality: A year in review. PHYSICA D. NONLINEAR PHENOMENA 2021; 425:132968. [PMID: 34121785 PMCID: PMC8183049 DOI: 10.1016/j.physd.2021.132968] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2021] [Revised: 05/10/2021] [Accepted: 06/01/2021] [Indexed: 05/21/2023]
Abstract
This paper introduces new methods to study the changing dynamics of COVID-19 cases and deaths among the 50 worst-affected countries throughout 2020. First, we analyse the trajectories and turning points of rolling mortality rates to understand at which times the disease was most lethal. We demonstrate five characteristic classes of mortality rate trajectories and determine structural similarity in mortality trends over time. Next, we introduce a class of virulence matrices to study the evolution of COVID-19 cases and deaths on a global scale. Finally, we introduce three-way inconsistency analysis to determine anomalous countries with respect to three attributes: countries' COVID-19 cases, deaths and human development indices. We demonstrate the most anomalous countries across these three measures are Pakistan, the United States and the United Arab Emirates.
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Affiliation(s)
- Nick James
- School of Mathematics and Statistics, University of Melbourne, Victoria, Australia
| | - Max Menzies
- Yau Mathematical Sciences Centre, Tsinghua University, Beijing, China
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11
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Kröger M, Turkyilmazoglu M, Schlickeiser R. Explicit formulae for the peak time of an epidemic from the SIR model. Which approximant to use? PHYSICA D. NONLINEAR PHENOMENA 2021; 425:132981. [PMID: 34188342 PMCID: PMC8225312 DOI: 10.1016/j.physd.2021.132981] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2021] [Revised: 06/15/2021] [Accepted: 06/16/2021] [Indexed: 05/04/2023]
Abstract
An analytic evaluation of the peak time of a disease allows for the installment of effective epidemic precautions. Recently, an explicit analytic, approximate expression (MT) for the peak time of the fraction of infected persons during an outbreak within the susceptible-infectious-recovered/removed (SIR) model had been presented and discussed (Turkyilmazoglu, 2021). There are three existing approximate solutions (SK-I, SK-II, and CG) of the semi-time SIR model in its reduced formulation that allow one to come up with different explicit expressions for the peak time of the infected compartment (Schlickeiser and Kröger, 2021; Carvalho and Gonçalves, 2021). Here we compare the four expressions for any choice of SIR model parameters and find that SK-I, SK-II and CG are more accurate than MT as long as the amount of population to which the SIR model is applied exceeds hundred by far (countries, ss, cities). For small populations with less than hundreds of individuals (families, small towns), however, the approximant MT outperforms the other approximants. To be able to compare the various approaches, we clarify the equivalence between the four-parametric dimensional SIR equations and their two-dimensional dimensionless analogue. Using Covid-19 data from various countries and sources we identify the relevant regime within the parameter space of the SIR model.
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Affiliation(s)
- Martin Kröger
- Polymer Physics, Department of Materials, ETH Zurich, Leopold-Ruzicka-Weg 4, 8093 Zurich, Switzerland
| | - Mustafa Turkyilmazoglu
- Department of Mathematics, Hacettepe University, Beytepe, 06532, Ankara, Turkey
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
| | - Reinhard Schlickeiser
- Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, 44780 Bochum, Germany
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstr. 15, 24118 Kiel, Germany
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Pérez-García VM. Nonlinear science against the COVID-19 pandemic. PHYSICA D. NONLINEAR PHENOMENA 2021; 424:132946. [PMID: 33967364 PMCID: PMC8086261 DOI: 10.1016/j.physd.2021.132946] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2021] [Accepted: 04/26/2021] [Indexed: 06/12/2023]
Abstract
This special issue showcases recent uses of mathematical and nonlinear science methods in the study of different problems arising in the context of the COVID-19 pandemic. The sixteen original research papers included in this collection span a wide spectrum of studies including classical epidemiological models, new models accounting for COVID-19 specificities, non-pharmaceutical control measures, network models and other problems related to the pandemic.
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Affiliation(s)
- Víctor M Pérez-García
- Mathematical Oncology Laboratory (MOLAB), Departamento de Matemáticas, E. T. S. I. Industriales and Instituto de Matemática Aplicada a la Ciencia y la Ingeniería, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
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13
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Modeling of COVID-19 propagation with compartment models. MATHEMATISCHE SEMESTERBERICHTE 2021; 68:181-219. [PMID: 34795464 PMCID: PMC8564799 DOI: 10.1007/s00591-021-00312-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/09/2021] [Accepted: 10/08/2021] [Indexed: 12/05/2022]
Abstract
The current pandemic is a great challenge for several research areas. In addition to virology research, mathematical models and simulations can be a valuable contribution to the understanding of the dynamics of the pandemic and can give recommendations to both physicians and politicians. In this paper we give an overview about mathematical models to describe the pandemic by differential equations. As a matter of principle the historic origin of the epidemic growth models will be remembered. Moreover we discuss models for the actual pandemic of 2020/2021. This will be done based on actual data of people infected with COVID-19 from the European Centre for Disease Prevention and Control (ECDC), input parameters of mathematical models will be determined and applied. These parameters will be estimated for the UK, Italy, Spain, and Germany and used in a SIR-type model. As a basis for the model’s calibration, the initial exponential growth phase of the COVID-19 pandemic in the named countries is used. Strategies for the commencing and ending of social and economic shutdown measures are discussed. To respect heterogeneity of the people density in the different federal states of Germany diffusion effects are considered.
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14
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Liu S, Li MY. Epidemic models with discrete state structures. PHYSICA D. NONLINEAR PHENOMENA 2021; 422:132903. [PMID: 33782628 PMCID: PMC7989216 DOI: 10.1016/j.physd.2021.132903] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2020] [Revised: 03/07/2021] [Accepted: 03/09/2021] [Indexed: 05/12/2023]
Abstract
The state of an infectious disease can represent the degree of infectivity of infected individuals, or susceptibility of susceptible individuals, or immunity of recovered individuals, or a combination of these measures. When the disease progression is long such as for HIV, individuals often experience switches among different states. We derive an epidemic model in which infected individuals have a discrete set of states of infectivity and can switch among different states. The model also incorporates a general incidence form in which new infections are distributed among different disease states. We discuss the importance of the transmission-transfer network for infectious diseases. Under the assumption that the transmission-transfer network is strongly connected, we establish that the basic reproduction number R 0 is a sharp threshold parameter: if R 0 ≤ 1 , the disease-free equilibrium is globally asymptotically stable and the disease always dies out; if R 0 > 1 , the disease-free equilibrium is unstable, the system is uniformly persistent and initial outbreaks lead to persistent disease infection. For a restricted class of incidence functions, we prove that there is a unique endemic equilibrium and it is globally asymptotically stable when R 0 > 1 . Furthermore, we discuss the impact of different state structures on R 0 , on the distribution of the disease states at the unique endemic equilibrium, and on disease control and preventions. Implications to the COVID-19 pandemic are also discussed.
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Affiliation(s)
- Suli Liu
- School of Mathematics, Jilin University, Changchun, Jilin Province, 130012, China
| | - Michael Y Li
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada
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15
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Turkyilmazoglu M. Explicit formulae for the peak time of an epidemic from the SIR model. PHYSICA D. NONLINEAR PHENOMENA 2021; 422:132902. [PMID: 33814655 PMCID: PMC7997702 DOI: 10.1016/j.physd.2021.132902] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Revised: 03/06/2021] [Accepted: 03/09/2021] [Indexed: 05/10/2023]
Abstract
Reducing the peak time of an epidemic disease in order for slowing down the eventual dynamics and getting prepared for the unavoidable epidemic wave is utmost significant to fight against the risks of a contagious epidemic disease. To serve to this purpose, the well-documented infection model of SIR is examined in the current research to propose an analytical approach for providing an explicit formula associated with a straightforward computation of peak time of outbreak. Initially, the time scale from the relevant autonomous SIR epidemic model is formulated analytically via an integral based on the fractions of susceptible and infected compartments. Afterwards, through a series expansion of the logarithmic term of the resultant integrand, the peak time is shown to rely upon the fraction of susceptible, the infectious ratio as well as the initial fractions of ill and susceptible individuals. The approximate expression is shown to rigorously capable of capturing the time threshold of illness for an epidemic from the semi-time SIR epidemiology. Otherwise, it is also successful to predict the peak time from a past history of a disease when all-time epidemic model is adopted. Accuracy of the derived expressions are initially confirmed by direct comparisons with recently reported approximate formulas in the literature. Several other epidemic disease samples including the COVID-19 often studied in the recent literature are eventually attacked with favourable performance of the presented formulae for assessing the peak time occurrence of an epidemic. A quick evaluation of the peak time of a disease certainly enables the governments to take early effective epidemic precautions.
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Affiliation(s)
- Mustafa Turkyilmazoglu
- Department of Mathematics, Hacettepe University, 06532 Beytepe, Ankara, Turkey
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
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16
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James N, Menzies M. Efficiency of communities and financial markets during the 2020 pandemic. CHAOS (WOODBURY, N.Y.) 2021; 31:083116. [PMID: 34470250 DOI: 10.1063/5.0054493] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
This paper investigates the relationship between the spread of the COVID-19 pandemic, the state of community activity, and the financial index performance across 20 countries. First, we analyze which countries behaved similarly in 2020 with respect to one of three multivariate time series: daily COVID-19 cases, Apple mobility data, and national equity index price. Next, we study the trajectories of all three of these attributes in conjunction to determine which exhibited greater similarity. Finally, we investigate whether country financial indices or mobility data responded more quickly to surges in COVID-19 cases. Our results indicate that mobility data and national financial indices exhibited the most similarity in their trajectories, with financial indices responding quicker. This suggests that financial market participants may have interpreted and responded to COVID-19 data more efficiently than governments. Furthermore, results imply that efforts to study community mobility data as a leading indicator for financial market performance during the pandemic were misguided.
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Affiliation(s)
- Nick James
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Victoria 3010, Australia
| | - Max Menzies
- Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China
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17
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A Local and Time Resolution of the COVID-19 Propagation—A Two-Dimensional Approach for Germany Including Diffusion Phenomena to Describe the Spatial Spread of the COVID-19 Pandemic. PHYSICS 2021. [DOI: 10.3390/physics3030033] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The understanding of factors that affect the dissemination of a viral infection is fundamental to help combat it. For instance, during the COVID-19 pandemic that changed the lives of people all over the world, one observes regions with different incidences of cases. One can speculate that population density might be one of the variables that affect the incidence of cases. In populous areas, such as big cities or congested urban areas, higher COVID-19 incidences could be observed than in rural regions. It is natural to think that if population density is such an important factor, then a gradient or difference in population density might lead to a diffusion process that will proceed until equilibrium is reached. The aim of this paper consists of the inclusion of a diffusion concept into the COVID-19 modeling. With this concept, one covers a gradient-driven transfer of the infection next to epidemic growth models (SIR-type models). This is discussed for a certain period of the German situation based on the quite different incidence data for the different federal states of Germany. With this ansatz, some phenomena of the actual development of the pandemic are found to be confirmed. The model provides a possibility to investigate certain scenarios, such as border-crossings or local spreading events, and their influence on the COVID-19 propagation. The resulting information can be a basis for the decisions of politicians and medical persons in charge of managing a pandemic.
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18
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Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations. PHYSICS 2021. [DOI: 10.3390/physics3020028] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
With the vaccination against Covid-19 now available, how vaccination campaigns influence the mathematical modeling of epidemics is quantitatively explored. In this paper, the standard susceptible-infectious-recovered/removed (SIR) epidemic model is extended to a fourth compartment, V, of vaccinated persons. This extension involves the time t-dependent effective vaccination rate, v(t), that regulates the relationship between susceptible and vaccinated persons. The rate v(t) competes with the usual infection, a(t), and recovery, μ(t), rates in determining the time evolution of epidemics. The occurrence of a pandemic outburst with rising rates of new infections requires k+b<1−2η, where k=μ(0)/a(0) and b=v(0)/a(0) denote the initial values for the ratios of the three rates, respectively, and η≪1 is the initial fraction of infected persons. Exact analytical inverse solutions t(Q) for all relevant quantities Q=[S,I,R,V] of the resulting SIRV model in terms of Lambert functions are derived for the semi-time case with time-independent ratios k and b between the recovery and vaccination rates to the infection rate, respectively. These inverse solutions can be approximated with high accuracy, yielding the explicit time-dependences Q(t) by inverting the Lambert functions. The values of the three parameters k, b and η completely determine the reduced time evolution of the SIRV-quantities Q(τ). The influence of vaccinations on the total cumulative number and the maximum rate of new infections in different countries is calculated by comparing with monitored real time Covid-19 data. The reduction in the final cumulative fraction of infected persons and in the maximum daily rate of new infections is quantitatively determined by using the actual pandemic parameters in different countries. Moreover, a new criterion is developed that decides on the occurrence of future Covid-19 waves in these countries. Apart from in Israel, this can happen in all countries considered.
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James N. Dynamics, behaviours, and anomaly persistence in cryptocurrencies and equities surrounding COVID-19. PHYSICA A 2021; 570:125831. [PMID: 36570814 PMCID: PMC9758953 DOI: 10.1016/j.physa.2021.125831] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2021] [Revised: 01/28/2021] [Indexed: 05/14/2023]
Abstract
This paper uses new and recently introduced methodologies to study the similarity in the dynamics and behaviours of cryptocurrencies and equities surrounding the COVID-19 pandemic. We study two collections; 45 cryptocurrencies and 72 equities, both independently and in conjunction. First, we examine the evolution of cryptocurrency and equity market dynamics, with a particular focus on their change during the COVID-19 pandemic. We demonstrate markedly more similar dynamics during times of crisis. Next, we apply recently introduced methods to contrast trajectories, erratic behaviours, and extreme values among the two multivariate time series. Finally, we introduce a new framework for determining the persistence of market anomalies over time. Surprisingly, we find that although cryptocurrencies exhibit stronger collective dynamics and correlation in all market conditions, equities behave more similarly in their trajectories and extremes, and show greater persistence in anomalies over time.
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Affiliation(s)
- Nick James
- School of Mathematics and Statistics, University of Sydney, NSW, Australia
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20
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Kurkina ES, Koltsova EM. Mathematical Modeling of the Propagation of Covid-19 Pandemic Waves in the World. COMPUTATIONAL MATHEMATICS AND MODELING 2021. [PMCID: PMC8287549 DOI: 10.1007/s10598-021-09523-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We develop a mathematical model of the coronavirus propagation in different countries (Brazil, India, US, Japan, Israel, Spain, Sweden), in the city of Moscow, and across the world. The pandemic spreads by a highly complex dynamics because it occurs in open nonhomogeneous systems where new infection foci erupt from time to time, triggering new transmission chains from infected to susceptible people. In general, statistical data collected as cumulative and epidemic curves are a superposition of many distinct local pandemic waves. In our modeling, we use the system of Feigenbaum’s discrete logistic equations (a logistic map) that describes the variation of the total number of infected over time. We show that this is the optimal model for the description of pandemic propagation in open nonhomogeneous systems with large errors in statistical data. We develop a procedure for isolating local waves, determining their model parameters, and predicting further evolution of each wave. We show that this model provides a good description of the statistical data and makes realistic forecasts. The forecast horizon depends on the degree of system closure and homogeneity. We calculate the start and end times of each wave, the peak, and the total number of infected in the current wave.
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Affiliation(s)
- E. S. Kurkina
- Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia
- Mendeleev Russian Chemical-Engineering University, Moscow, Russia
| | - E. M. Koltsova
- Mendeleev Russian Chemical-Engineering University, Moscow, Russia
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21
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James N, Menzies M. Association between COVID-19 cases and international equity indices. PHYSICA D. NONLINEAR PHENOMENA 2021; 417:132809. [PMID: 33362322 PMCID: PMC7756167 DOI: 10.1016/j.physd.2020.132809] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Revised: 11/17/2020] [Accepted: 11/17/2020] [Indexed: 05/03/2023]
Abstract
This paper analyzes the impact of COVID-19 on the populations and equity markets of 92 countries. We compare country-by-country equity market dynamics to cumulative COVID-19 case and death counts and new case trajectories. First, we examine the multivariate time series of cumulative cases and deaths, particularly regarding their changing structure over time. We reveal similarities between the case and death time series, and key dates that the structure of the time series changed. Next, we classify new case time series, demonstrate five characteristic classes of trajectories, and quantify discrepancy between them with respect to the behavior of waves of the disease. Finally, we show there is no relationship between countries' equity market performance and their success in managing COVID-19. Each country's equity index has been unresponsive to the domestic or global state of the pandemic. Instead, these indices have been highly uniform, with most movement in March.
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Affiliation(s)
- Nick James
- School of Mathematics and Statistics, University of Sydney, NSW, Australia
| | - Max Menzies
- Yau Mathematical Sciences Center, Tsinghua University, Beijing, China
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22
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Padhy S, Dimri VP. Apparent scaling of virus surface roughness-An example from the pandemic SARS-nCoV. PHYSICA D. NONLINEAR PHENOMENA 2020; 414:132704. [PMID: 32901164 PMCID: PMC7471937 DOI: 10.1016/j.physd.2020.132704] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2020] [Revised: 08/24/2020] [Accepted: 08/25/2020] [Indexed: 05/08/2023]
Abstract
This paper investigates the scaling of the surface roughness of coronavirus, including the SARS-nCoV based on fractal and spectral analyses of their published electron microscopy images. The box-counting fractal dimensions obtained are subjected to ANOVA tests for statistical significance. Results show that the SARS-nCoV particles could not statistically be resolved by their shape on the basis of the fractal dimension values, but they could be distinguished from the earlier SARS-CoV particles. MANOVA test results require interaction of factors used for classifying virions into different types. The topological entropies, a measure of randomness in a system, measured for the images of varying size show correlation with the fractal dimensions. Spectral analyses of our data show a departure from power-law self-similarity, suggesting an apparent scaling of surface roughness over a band of maximum an order of magnitude. The spectral crossover that corresponds to characteristic length scale may represent average viral size. Our results may be useful in inferring the nature of surface-contact between the viral and human cell, causing infection and also in providing clues for new drugs, although it is too early to say. In addition, limitations of this study, including possible ways to avoid the bias in scaling exponents due to the use of different techniques are discussed.
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Affiliation(s)
- Simanchal Padhy
- CSIR-National Geophysical Research Institute, Hyderabad, India
| | - Vijay P Dimri
- CSIR-National Geophysical Research Institute, Hyderabad, India
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