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

Front propagation in a spatial system of weakly interacting networks

We consider the spread of epidemic in a spatial metapopulation system consisting of weakly interacting patches. Each local patch is represented by a network with a certain node degree distribution and individuals can migrate between neighboring patches. Stochastic particle simulations of the SIR model show that after a short transient, the spatial spread of epidemic has a form of a propagating front. A theoretical analysis shows that the speed of front propagation depends on the effective diffusion coefficient and on the local proliferation rate similarly to fronts described by the Fisher-Kolmogorov equation. To determine the speed of front propagation, first, the early-time dynamics in a local patch is computed analytically by employing degree based approximation for the case of a constant disease duration. The resulting delay differential equation is solved for early times to obtain the local growth exponent. Next, the reaction diffusion equation is derived from the effective master equation and the effective diffusion coefficient and the overall proliferation rate are determined. Finally, the fourth order derivative in the reaction diffusion equation is taken into account to obtain the discrete correction to the front propagation speed. The analytical results are in a good agreement with the results of stochastic particle simulations.

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 of resource allocation strategies on spatial spread of epidemics

Medical resources are crucial in mitigating epidemics, especially during pandemics such as the ongoing COVID-19. Thereby, reasonable resource deployment inevitably plays a significant role in suppressing the epidemic under limited resources. When an epidemic breaks out, people can produce resources for self-protection or donate resources to help others for treatment. That is, the exchange of resources also affects the transmission between individuals, thus, altering the epidemic dynamics. To understand factors on resource deployment and the interplay between resource and transmission we construct a metapopulation network model with resource allocation. Our results indicate actively or promptly donating resources is not helpful to suppress the epidemic under both homogeneous population distribution and heterogeneous population distribution. Besides, strengthening the speed of resources production can significantly increase the recovery rate so that they reduce the final outbreak size. These results may provide policy guidance toward epidemic containment.

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.

A multi-source global-local model for epidemic management

The Effective Reproduction Number Rt provides essential information for the management of an epidemic/pandemic. Projecting Rt into the future could further assist in the management process. This article proposes a methodology based on exposure scenarios to perform such a procedure. The method utilizes a compartmental model and its adequate parametrization; a way to determine suitable parameters for this model in México's case is detailed. In conjunction with the compartmental model, the projection of Rt permits estimating unobserved variables, such as the size of the asymptomatic population, and projecting into the future other relevant variables, like the active hospitalizations, using scenarios. The uses of the proposed methodologies are exemplified by analyzing the pandemic in a Mexican state; the main quantities derived from the compartmental model, such as the active and total cases, are included in the analysis. This article also presents a national summary based on the methodologies to illustrate how these procedures could be further exploited. The supporting information includes an application of the proposed methods to a metropolitan area to show that it also works well at other demographic disaggregation levels. The procedures developed in this article shed light on how to develop an effective surveillance system when information is incomplete and can be applied in cases other than México's.

Understanding small Chinese cities as COVID-19 hotspots with an urban epidemic hazard index

Multiple small- to middle-scale cities, mostly located in northern China, became epidemic hotspots during the second wave of the spread of COVID-19 in early 2021. Despite qualitative discussions of potential social-economic causes, it remains unclear how this unordinary pattern could be substantiated with quantitative explanations. Through the development of an urban epidemic hazard index (EpiRank) for Chinese prefectural districts, we came up with a mathematical explanation for this phenomenon. The index is constructed via epidemic simulations on a multi-layer transportation network interconnecting local SEIR transmission dynamics, which characterizes intra- and inter-city population flow with a granular mathematical description. Essentially, we argue that these highlighted small towns possess greater epidemic hazards due to the combined effect of large local population and small inter-city transportation. The ratio of total population to population outflow could serve as an alternative city-specific indicator of such hazards, but its effectiveness is not as good as EpiRank, where contributions from other cities in determining a specific city's epidemic hazard are captured via the network approach. Population alone and city GDP are not valid signals for this indication. The proposed index is applicable to different epidemic settings and can be useful for the risk assessment and response planning of urban epidemic hazards in China. The model framework is modularized and the analysis can be extended to other nations.

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.

Universal features of epidemic models under social distancing guidelines

Social distancing as a form of nonpharmaceutical intervention has been enacted in many countries as a form of mitigating the spread of COVID-19. There has been a large interest in mathematical modeling to aid in the prediction of both the total infected population and virus-related deaths, as well as to aid government agencies in decision making. As the virus continues to spread, there are both economic and sociological incentives to minimize time spent with strict distancing mandates enforced, and/or to adopt periodically relaxed distancing protocols, which allow for scheduled economic activity. The main objective of this study is to reduce the disease burden in a population, here measured as the peak of the infected population, while simultaneously minimizing the length of time the population is socially distanced, utilizing both a single period of social distancing as well as periodic relaxation. We derive a linear relationship among the optimal start time and duration of a single interval of social distancing from an approximation of the classic epidemic SIR model. Furthermore, we see a sharp phase transition region in start times for a single pulse of distancing, where the peak of the infected population changes rapidly; notably, this transition occurs well before one would intuitively expect. By numerical investigation of more sophisticated epidemiological models designed specifically to describe the COVID-19 pandemic, we see that all share remarkably similar dynamic characteristics when contact rates are subject to periodic or one-shot changes, and hence lead us to conclude that these features are universal in epidemic models. On the other hand, the nonlinearity of epidemic models leads to non-monotone behavior of the peak of infected population under periodic relaxation of social distancing policies. This observation led us to hypothesize that an additional single interval social distancing at a proper time can significantly decrease the infected peak of periodic policies, and we verified this improvement numerically. While synchronous quarantine and social distancing mandates across populations effectively minimize the spread of an epidemic over the world, relaxation decisions should not be enacted at the same time for different populations.