Epidemic outbreaks in two-scale community networks

A novel geo-hierarchical population mobility model for spatial spreading of resurgent epidemics

Computational models for large, resurgent epidemics are recognized as a crucial tool for predicting the spread of infectious diseases. It is widely agreed, that such models can be augmented with realistic multiscale population models and by incorporating human mobility patterns. Nevertheless, a large proportion of recent studies, aimed at better understanding global epidemics, like influenza, measles, H1N1, SARS, and COVID-19, underestimate the role of heterogeneous mixing in populations, characterized by strong social structures and geography. Motivated by the reduced tractability of studies employing homogeneous mixing, which make conclusions hard to deduce, we propose a new, very fine-grained model incorporating the spatial distribution of population into geographical settlements, with a hierarchical organization down to the level of households (inside which we assume homogeneous mixing). In addition, population is organized heterogeneously outside households, and we model the movement of individuals using travel distance and frequency parameters for inter- and intra-settlement movement. Discrete event simulation, employing an adapted SIR model with relapse, reproduces important qualitative characteristics of real epidemics, like high variation in size and temporal heterogeneity (e.g., waves), that are challenging to reproduce and to quantify with existing measures. Our results pinpoint an important aspect, that epidemic size is more sensitive to the increase in distance of travel, rather that the frequency of travel. Finally, we discuss implications for the control of epidemics by integrating human mobility restrictions, as well as progressive vaccination of individuals.

Epidemic Spread on One-Way Circular-Coupled Networks

Real epidemic spreading networks are often composed of several kinds of complex networks interconnected with each other, such as Lyme disease, and the interrelated networks may have different topologies and epidemic dynamics. Moreover, most human infectious diseases are derived from animals, and zoonotic infections always spread on directed interconnected networks. So, in this article, we consider the epidemic dynamics of zoonotic infections on a unidirectional circular-coupled network. Here, we construct two unidirectional three-layer circular interactive networks, one model has direct contact between interactive networks, the other model describes diseases transmitted through vectors between interactive networks, which are established by introducing the heterogeneous mean-field approach method. Then we obtain the basic reproduction numbers and stability of equilibria of the two models. Through mathematical analysis and numerical simulations, it is found that basic reproduction numbers of the models depend on the infection rates, infection periods, average degrees, and degree ratios. Numerical simulations illustrate and expand these theoretical results very well.

Structural transition in interdependent networks with regular interconnections

Networks are often made up of several layers that exhibit diverse degrees of interdependencies. An interdependent network consists of a set of graphs G that are interconnected through a weighted interconnection matrix B, where the weight of each intergraph link is a non-negative real number p. Various dynamical processes, such as synchronization, cascading failures in power grids, and diffusion processes, are described by the Laplacian matrix Q characterizing the whole system. For the case in which the multilayer graph is a multiplex, where the number of nodes in each layer is the same and the interconnection matrix B=pI, I being the identity matrix, it has been shown that there exists a structural transition at some critical coupling p^{*}. This transition is such that dynamical processes are separated into two regimes: if p>p^{*}, the network acts as a whole; whereas when p<p^{*}, the network operates as if the graphs encoding the layers were isolated. In this paper, we extend and generalize the structural transition threshold p^{*} to a regular interconnection matrix B (constant row and column sum). Specifically, we provide upper and lower bounds for the transition threshold p^{*} in interdependent networks with a regular interconnection matrix B and derive the exact transition threshold for special scenarios using the formalism of quotient graphs. Additionally, we discuss the physical meaning of the transition threshold p^{*} in terms of the minimum cut and show, through a counterexample, that the structural transition does not always exist. Our results are one step forward on the characterization of more realistic multilayer networks and might be relevant for systems that deviate from the topological constraints imposed by multiplex networks.

Modeling and analysis of epidemic spreading on community networks with heterogeneity

A large number of real world networks exhibit community structure, and different communities may often possess heterogeneity. In this paper, considering the heterogeneity among communities, we construct a new community network model in which the communities show significant differences in average degree. Based on this heterogeneous community network, we propose a novel mathematical epidemic model for each community and study the epidemic dynamics in this network model. We find that the location of the initial infection node only affects the spreading velocity and barely influences the epidemic prevalence. And the epidemic threshold of entire network decreases with the increase of heterogeneity among communities. Moreover, the epidemic prevalence increases with the increase of heterogeneity around the epidemic threshold, while the converse situation holds when the infection rate is much greater than the epidemic threshold.

EPIDEMIC SPREADING ON THREE-LAYER INTERDEPENDENT NETWORKS

Many epidemic diseases spread among three different populations with different contact patterns and infection rates. In response to such diseases, we propose two new types of three-layer interdependent networks — string-coupled networks and circular-coupled networks. We investigate an epidemic spreading on the two types of interdependent networks, propose two mathematical models through heterogeneous mean field approach and prove global stability of the disease-free and endemic equilibria. Through theoretical and numerical analysis, we find the following: the increase of each infection rate affects effectively only its own subnetwork and neighbors; in a string-coupled network, the middle subnetwork has bigger impact on the basic reproduction number than the end subnetworks with the growth of network size or infection rates; the basic reproduction number on a circular-coupled network is larger than that on a string-coupled network for a fixed network size; but the change of the basic reproduction number (or the average infection densities) is almost the same on both string-coupled and circular-coupled networks with the increasing of certain infection rate.

Modeling and analysis of epidemic spreading on community network with node's birth and death

In this paper, a modified susceptible infected susceptible (SIS) epidemic model is proposed on community structure networks considering birth and death of node. For the existence of node's death would change the topology of global network, the characteristic of network with death rate is discussed. Then we study the epidemiology behavior based on the mean-field theory and derive the relationships between epidemic threshold and other parameters, such as modularity coefficient, birth rate and death rates (caused by disease or other reasons). In addition, the stability of endemic equilibrium is analyzed. Theoretical analysis and simulations show that the epidemic threshold increases with the increase of two kinds of death rates, while it decreases with the increase of the modularity coefficient and network size.

Epidemic spreading on complex networks with community structures

Many real-world networks display a community structure. We study two random graph models that create a network with similar community structure as a given network. One model preserves the exact community structure of the original network, while the other model only preserves the set of communities and the vertex degrees. These models show that community structure is an important determinant of the behavior of percolation processes on networks, such as information diffusion or virus spreading: the community structure can both enforce as well as inhibit diffusion processes. Our models further show that it is the mesoscopic set of communities that matters. The exact internal structures of communities barely influence the behavior of percolation processes across networks. This insensitivity is likely due to the relative denseness of the communities.

Epidemics on networks with heterogeneous population and stochastic infection rates

In this paper we study the diffusion of an SIS-type epidemics on a network under the presence of a random environment, that enters in the definition of the infection rates of the nodes. Accordingly, we model the infection rates in the form of independent stochastic processes. To analyze the problem, we apply a mean field approximation, which allows to get a stochastic differential equations for the probability of infection in each node, and classical tools about stability, which require to find suitable Lyapunov's functions. Here, we find conditions which guarantee, respectively, extinction and stochastic persistence of the epidemics. We show that there exists two regions, given in terms of the coefficients of the model, one where the system goes to extinction almost surely, and the other where it is stochastic permanent. These two regions are, unfortunately, not adjacent, as there is a gap between them, whose extension depends on the specific level of noise. In this last region, we perform numerical analysis to suggest the true behavior of the solution.

Beyond Contact Tracing: Community-Based Early Detection for Ebola Response

INTRODUCTION

The 2014 Ebola outbreak in West Africa raised many questions about the control of infectious disease in an increasingly connected global society. Limited availability of contact information made contact tracing diffcult or impractical in combating the outbreak. 

METHODS

We consider the development of multi-scale public health strategies that act on individual and community levels. We simulate policies for community-level response aimed at early screening all members of a community, as well as travel restrictions to prevent inter-community transmission. 

RESULTS

Our analysis shows the policies to be effective even at a relatively low level of compliance and for a variety of local and long range contact transmission networks. In our simulations, 40% of individuals conforming to these policies is enough to stop the outbreak. Simulations with a 50% compliance rate are consistent with the case counts in Liberia during the period of rapid decline after mid September, 2014. We also find the travel restriction to be effective at reducing the risks associated with compliance substantially below the 40% level, shortening the outbreak and enabling efforts to be focused on affected areas. 

DISCUSSION

Our results suggest that the multi-scale approach can be used to further evolve public health strategy for defeating emerging epidemics.

Community Size Effects on Epidemic Spreading in Multiplex Social Networks

The dynamical process of epidemic spreading has drawn much attention of the complex network community. In the network paradigm, diseases spread from one person to another through the social ties amongst the population. There are a variety of factors that govern the processes of disease spreading on the networks. A common but not negligible factor is people's reaction to the outbreak of epidemics. Such reaction can be related information dissemination or self-protection. In this work, we explore the interactions between disease spreading and population response in terms of information diffusion and individuals' alertness. We model the system by mapping multiplex networks into two-layer networks and incorporating individuals' risk awareness, on the assumption that their response to the disease spreading depends on the size of the community they belong to. By comparing the final incidence of diseases in multiplex networks, we find that there is considerable mitigation of diseases spreading for full phase of spreading speed when individuals' protection responses are introduced. Interestingly, the degree of community overlap between the two layers is found to be critical factor that affects the final incidence. We also analyze the consequences of the epidemic incidence in communities with different sizes and the impacts of community overlap between two layers. Specifically, as the diseases information makes individuals alert and take measures to prevent the diseases, the effective protection is more striking in small community. These phenomena can be explained by the multiplexity of the networked system and the competition between two spreading processes.

A three-scale network model for the early growth dynamics of 2014 west Africa ebola epidemic

BACKGROUND

In mid-October 2014, the number of cases of the West Africa Ebola virus epidemic in Guinea, Sierra Leone and Liberia exceeded 9,000 cases. The early growth dynamics of the epidemic has been qualitatively different for each of the three countries. However, it is important to understand these disparate dynamics as trends of a single epidemic spread over regions with similar geographic and cultural aspects, with likely common parameters for transmission rates and reproduction number R0.

METHODS

We combine a discrete, stochastic SEIR model with a three-scale community network model to demonstrate that the different regional trends may be explained by different community mixing rates. Heuristically, the effect of different community mixing rates may be understood as the observation that two individuals infected by the same chain of transmission are more likely to share the same contacts in a less-mixed community. Local saturation effects occur as the contacts of an infected individual are more likely to already be exposed by the same chain of transmission.

RESULTS

The effects of community mixing, together with stochastic effects, can explain the qualitative difference in the growth of Ebola virus cases in each country, and why the probability of large outbreaks may have recently increased. An increase in the rate of Ebola cases in Guinea in late August, and a local fitting of the transient dynamics of the Ebola cases in Liberia, suggests that the epidemic in Liberia has been more severe, and the epidemic in Guinea is worsening, due to discrete seeding events as the epidemic spreads into new communities.

CONCLUSIONS

A relatively simple network model provides insight on the role of local effects such as saturation that would be difficult to otherwise quantify. Our results predict that exponential growth of an epidemic is driven by the exposure of new communities, underscoring the importance of limiting this spread.