Interplay between epidemic spread and information propagation on metapopulation networks

On epidemic spreading in metapopulation networks with time-varying contact patterns

Considering that people may change their face-to-face communication patterns with others depending on the season, we propose an epidemic model that incorporates a time-varying contact rate on a metapopulation network and its second-neighbor network. To describe the time-varying contact mode, we utilize a switched system and define two forms of the basic reproduction number corresponding to two different restrictions. We provide the theoretical proof for the stability of the disease-free equilibrium and confirm periodic stability conditions using simulations. The simulation results reveal that as the period of the switched system lengthens, the amplitude of the final infected density increases; however, the peak infected density within a specific period remains relatively unchanged. Interestingly, as the basic reproduction number grows, the amplitude of the final infected density within a period gradually rises to its maximum and then declines. Moreover, the contact rate that occupies a longer duration within a single period has a more significant influence on epidemic spreading. As the values of different contact rates progressively increase, the recovery rate, natural birth rate, and natural death rate all decrease, leading to a larger final infection density.

Epidemic dynamics on metapopulation networks with node2vec mobility

Metapopulation models have been a powerful tool for both theorizing and simulating epidemic dynamics. In a metapopulation model, one considers a network composed of subpopulations and their pairwise connections, and individuals are assumed to migrate from one subpopulation to another obeying a given mobility rule. While how different mobility rules affect epidemic dynamics in metapopulation models has been studied, there have been relatively few efforts on comparison of the effects of simple (i.e., unbiased) random walks and more complex mobility rules. Here we study a susceptible-infectious-susceptible (SIS) dynamics in a metapopulation model in which individuals obey a parametric second-order random-walk mobility rule called the node2vec. We map the second-order mobility rule of the node2vec to a first-order random walk in a network whose each node is a directed edge connecting a pair of subpopulations and then derive the epidemic threshold. For various networks, we find that the epidemic threshold is large (therefore, epidemic spreading tends to be suppressed) when the individuals infrequently backtrack or infrequently visit the common neighbors of the currently visited and the last visited subpopulations than when the individuals obey the simple random walk. The amount of change in the epidemic threshold induced by the node2vec mobility is in general not as large as, but is sometimes comparable with, the one induced by the change in the diffusion rate for individuals.

Network structure-based interventions on spatial spread of epidemics in metapopulation networks

Mathematical modeling of epidemics is fundamental to understand the mechanism of the disease outbreak and provides helpful indications for effectiveness of interventions for policy makers. The metapopulation network model has been used in the analysis of epidemic dynamics by taking individual migration between patches into account. However, so far, most of the previous studies unrealistically assume that transmission rates within patches are the same, neglecting the nonuniformity of intervention measures in hindering epidemics. Here, based on the assumption that interventions deployed in a patch depend on its population size or economic level, which have shown a positive correlation with the patch's degree in networks, we propose a metapopulation network model to explore a network structure-based intervention strategy, aiming at understanding the interplay between intervention strategy and other factors including mobility patterns, initial population, as well as the network structure. Our results demonstrate that interventions to patches with different intensity are able to suppress the epidemic spreading in terms of both the epidemic threshold and the final epidemic size. Specifically, the intervention strategy targeting the patches with high degree is able to efficiently suppress epidemics. In addition, a detrimental effect is also observed depending on the interplay between the intervention measures and the initial population distribution. Our study opens a path for understanding epidemic dynamics and provides helpful insights into the implementation of countermeasures for the control of epidemics in reality.

Intervention threshold for epidemic control in susceptible-infected-recovered metapopulation models

Metapopulation epidemic models describe epidemic dynamics in networks of spatially distant patches connected via pathways for migration of individuals. In the present study, we deal with a susceptible-infected-recovered (SIR) metapopulation model where the epidemic process in each patch is represented by an SIR model and the mobility of individuals is assumed to be a homogeneous diffusion. We consider two types of patches including high-risk and low-risk ones under the assumption that a local patch is changed from a high-risk one to a low-risk one by an intervention. We theoretically analyze the intervention threshold which indicates the critical fraction of low-risk patches for preventing a global epidemic outbreak. We show that an intervention targeted to high-degree patches is more effective for epidemic control than a random intervention. The theoretical results are validated by Monte Carlo simulations for synthetic and realistic scale-free patch networks. The theoretical results also reveal that the intervention threshold depends on the human mobility network and the mobility rate. Our approach is useful for exploring better local interventions aimed at containment of epidemics.

Infectious diseases spreading on a metapopulation network coupled with its second-neighbor network

Traditional infectious diseases models on metapopulation networks focus on direct transportations (e.g., direct flights), ignoring the effect of indirect transportations. Based on global aviation network, we turn the problem of indirect flights into a question of second neighbors, and propose a susceptible-infectious-susceptible model to study disease transmission on a connected metapopulation network coupled with its second-neighbor network (SNN). We calculate the basic reproduction number, which is independent of human mobility, and we prove the global stability of disease-free and endemic equilibria of the model. Furthermore, the study shows that the behavior that all travelers travel along the SNN may hinder the spread of disease if the SNN is not connected. However, the behavior that individuals travel along the metapopulation network coupled with its SNN contributes to the spread of disease. Thus for an emerging infectious disease, if the real network and its SNN keep the same connectivity, indirect transportations may be a potential threat and need to be controlled. Our work can be generalized to high-speed train and rail networks, which may further promote other research on metapopulation networks.

Epidemic spreading on metapopulation networks including migration and demographics

Epidemic dynamics in a structured population has been widely investigated in recent years by utilizing the metapopulation framework with a reaction-diffusion approach. In this paper, we study epidemic spreading on metapopulation networks, including migration and demographics, wherein population dynamics in each node (a patch) follows the logistic model with a heterogeneous carrying capacity. The epidemic threshold is theoretically calculated at a mean-field level and is then evaluated by Monte Carlo simulations. It is shown that heterogeneity of carrying capacity drastically decreases the threshold, and conversely increasing the migration rate slightly increases the threshold. Interestingly, we observe Monte Carlo simulations showing the effect of heterogeneity of carrying capacity and migration on the epidemic prevalence above the epidemic threshold. Heterogeneity of carrying capacity enhances epidemic spreading in the initial stage, but has no impact on the final infection density. The migration rate has a pronounced impact on both temporal spreading behaviour and endemic state.

Moment closure of infectious diseases model on heterogeneous metapopulation network

The global transmission of infectious diseases poses huge threats to human. Traditional heterogeneous mean-field models on metapopulation networks ignore the heterogeneity of individuals who are in different disease states in subpopulations with the same degree, resulting in inaccuracy in predicting the spread of disease. In this paper, we take heterogeneity of susceptible and infectious individuals in subpopulations with the same degree into account, and propose a deterministic unclosed general model according to Markov process on metapopulation networks to curve the global transmission of diseases precisely. Then we make the general model closed by putting forward two common assumptions: a two-dimensional constant distribution and a two-dimensional log-normal distribution, where the former is equivalent to the heterogeneous mean-field model, and the latter is a system of weighted ordinary differential equations. Further we make a stability analysis for two closed models and illustrate the results by numerical simulations. Next, we conduct a series of numerical simulations and stochastic simulations. Results indicate that our general model extends and optimizes the mean-field model. Finally, we investigate the impacts of total mobility rate on disease transmission and find that timely and comprehensive travel restriction in the early stage is an effective prevention and control of infectious diseases.