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

Indirect transmission and disinfection strategies on heterogeneous networks

Besides direct contacts of individuals, indirect contacts with environments being the medium is another route of epidemic transmission, which most previous studies have ignored. Disinfection is one of the most effective and commonly used measures to prevent and control epidemic spreading. In this paper, we propose a metapopulationlike model incorporating direct and indirect transmissions for susceptible-infected-susceptible-like epidemics on heterogeneous networks. Furthermore, we explore the epidemic spreading process with heterogeneous disinfection on both spatial and time dimensions. Specifically, we put forward three types of disinfection strategies, namely, the static disinfection strategy, the random time disinfection strategy, and the event-triggered disinfection strategy. Comparative analysis of the three strategies suggests that managers should prioritize disinfection resource allocation to large-flow environments, especially when disinfection resources are limited. In addition, timely disinfection of environments with infected visitors is an effective and economical strategy. Our model sheds light on the interplay dynamics of indirect transmission and disinfection and the results provide theoretical support for governors to select proper disinfection strategies in practical scenarios.

Intervention strategies for epidemic spreading on bipartite metapopulation networks

Intervention strategies are of great significance for controlling large-scale outbreaks of epidemics. Since the spread of epidemic depends largely on the movement of individuals and the heterogeneity of the network structure, understanding potential factors that affect the epidemic is fundamental for the design of reasonable intervention strategies to suppress the epidemic. So far, most of previous studies mainly consider intervention strategies on the network composed of a single type of locations, while ignoring the movement behavior of individuals to and from locations that are composed of different types, i.e., residences and public places, which often presents heterogeneous structure. In addition, the transmission rate in public places with different population flows is heterogeneous. Inspired by the above observation, we build a bipartite metapopulation network model and propose intervention strategies based on the importance of public places. With the Markovian Chain approach, we derive the epidemic threshold under intervention strategies. Experimental results show that, compared with the uniform intervention to residences or public places, nonuniform intervention to public places is more effective for suppressing the epidemic with an increased epidemic threshold. Specifically, interventions to public places with large degree can further suppress the epidemic. Our study opens a new path for understanding the spatial epidemic spread and provides guidance for the design of intervention strategies for epidemics in the future.

Identifying influential subpopulations in metapopulation epidemic models using message-passing theory

Identifying influential subpopulations in metapopulation epidemic models has far-reaching potential implications for surveillance and intervention policies of a global pandemic. However, there is a lack of methods to determine influential nodes in metapopulation models based on a rigorous mathematical background. In this study, we derive the message-passing theory for metapopulation modeling and propose a method to determine influential spreaders. Based on our analysis, we identify the most dangerous city as a potential seed of a pandemic when applied to real-world data. Moreover, we particularly assess the relative importance of various sources of heterogeneity at the subpopulation level, e.g., the number of connections and mobility patterns, to determine properties of spreading processes. We validate our theory with extensive numerical simulations on empirical and synthetic networks considering various mobility and transmission probabilities. We confirm that our theory can accurately predict influential subpopulations in metapopulation models.

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.

Optimal test-kit-based intervention strategy of epidemic spreading in heterogeneous complex networks

We propose a deterministic compartmental model of infectious disease that considers the test kits as an important ingredient for the suppression and mitigation of epidemics. A rigorous simulation (with an analytical argument) is provided to reveal the effective reduction of the final outbreak size and the peak of infection as a function of basic reproduction number in a single patch. Furthermore, to study the impact of long and short-distance human migration among the patches, we consider heterogeneous networks where the linear diffusive connectivity is determined by the network link structure. We numerically confirm that implementation of test kits in a fraction of nodes (patches) having larger degrees or betweenness centralities can reduce the peak of infection (as well as the final outbreak size) significantly. A next-generation matrix-based analytical treatment is provided to find out the critical transmission probability in the entire network for the onset of epidemics. Finally, the optimal intervention strategy is validated in two real networks: the global airport network and the transportation network of Kolkata, India.

Connectivity, reproduction number, and mobility interact to determine communities' epidemiological superspreader potential in a metapopulation network

Disease epidemic outbreaks on human metapopulation networks are often driven by a small number of superspreader nodes, which are primarily responsible for spreading the disease throughout the network. Superspreader nodes typically are characterized either by their locations within the network, by their degree of connectivity and centrality, or by their habitat suitability for the disease, described by their reproduction number (R). Here we introduce a model that considers simultaneously the effects of network properties and R on superspreaders, as opposed to previous research which considered each factor separately. This type of model is applicable to diseases for which habitat suitability varies by climate or land cover, and for direct transmitted diseases for which population density and mitigation practices influences R. We present analytical models that quantify the superspreader capacity of a population node by two measures: probability-dependent superspreader capacity, the expected number of neighboring nodes to which the node in consideration will randomly spread the disease per epidemic generation, and time-dependent superspreader capacity, the rate at which the node spreads the disease to each of its neighbors. We validate our analytical models with a Monte Carlo analysis of repeated stochastic Susceptible-Infected-Recovered (SIR) simulations on randomly generated human population networks, and we use a random forest statistical model to relate superspreader risk to connectivity, R, centrality, clustering, and diffusion. We demonstrate that either degree of connectivity or R above a certain threshold are sufficient conditions for a node to have a moderate superspreader risk factor, but both are necessary for a node to have a high-risk factor. The statistical model presented in this article can be used to predict the location of superspreader events in future epidemics, and to predict the effectiveness of mitigation strategies that seek to reduce the value of R, alter host movements, or both.

An overview of epidemic models with phase transitions to absorbing states running on top of complex networks

Dynamical systems running on the top of complex networks have been extensively investigated for decades. But this topic still remains among the most relevant issues in complex network theory due to its range of applicability. The contact process (CP) and the susceptible-infected-susceptible (SIS) model are used quite often to describe epidemic dynamics. Despite their simplicity, these models are robust to predict the kernel of real situations. In this work, we review concisely both processes that are well-known and very applied examples of models that exhibit absorbing-state phase transitions. In the epidemic scenario, individuals can be infected or susceptible. A phase transition between a disease-free (absorbing) state and an active stationary phase (where a fraction of the population is infected) are separated by an epidemic threshold. For the SIS model, the central issue is to determine this epidemic threshold on heterogeneous networks. For the CP model, the main interest is to relate critical exponents with statistical properties of the network.

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.

Epidemic in networked population with recurrent mobility pattern

The novel Coronavirus (COVID-19) has caused a global crisis and many governments have taken social measures, such as home quarantine and maintaining social distance. Many recent studies show that network structure and human mobility greatly influence the dynamics of epidemic spreading. In this paper, we utilize a discrete-time Markov chain approach and propose an epidemic model to describe virus propagation in the heterogeneous graph, which is used to represent individuals with intra social connections and mobility between individuals and common locations. There are two types of nodes, individuals and public places, and disease can spread by social contacts among individuals and people gathering in common areas. We give theoretical results about epidemic threshold and influence of isolation factor. Several numerical simulations are performed and experimental results further demonstrate the correctness of proposed model. Non-monotonic relationship between mobility possibility and epidemic threshold and differences between Erdös-Rényi and power-law social connections are revealed. In summary, our proposed approach and findings are helpful to analyse and prevent the epidemic spreading in networked population with recurrent mobility pattern.

Epidemic spreading in heterogeneous networks with recurrent mobility patterns

Much recent research has shown that network structure and human mobility have great influences on epidemic spreading. In this paper, we propose a discrete-time Markov chain method to model susceptible-infected-susceptible epidemic dynamics in heterogeneous networks. There are two types of locations, residences and common places, for which different infection mechanisms are adopted. We also give theoretical results about the impacts of important factors, such as mobility probability and isolation, on epidemic threshold. Numerical simulations are conducted, and experimental results support our analysis. In addition, we find that the dominations of different types of residences might reverse when mobility probability varies for some networks. In summary, the findings are helpful for policy making to prevent the spreading of epidemics.