Dynamical Modeling And Analysis Of Infectious Diaseases On Metapopulation Networks

Infectious diseases have always been threaten to human life and health and the stable development of society,and their spread cannot be separated from human mobility.With the integration of global economy,the long-distance movement of human beings becomes more frequent,which promotes the rapid and wide spread of infectious diseases,such as,Spanish flu during 1918-1919,Hong Kong flu in 1968,SARS in 2003,influenza A?H1N1?in 2009,and the current pandemic of coronavirus diseases 2019?COVID-19?.Metapopulation networks are one of the effective tools to study the large-scale spread of infectious diseases by coupling human mobility and disease transmission.Each node?also known as a subpopulation?respresents a well-defined spatial region,such as a country,a city,or a family;each link indicates individuals movement between two connected subpopulations.From the perspective of modeling methods and network structures,this paper derives and analyzes moment-closure metapopulation network model,studies the influence of metapopulation network structures formed by different mobility modes,such as human multi-step mobility mode and mobility mode under travel restriction,on the large-scale spread of infectious diseases,and applies a metapopulation network model to the prediction and assessment of prevention and control measures for COVID-19.In modeling method,based on the continuous time Markov chain,we derive the mathematical derivation of heterogeneous mean field model theoretically,which solves the foundational issue of heterogeneous mean field model;in theory,we investigate the effect of different network structures formed under different mobility modes on the spread of infectious diseases;on the application,based on the outbreak characteristics and prevention and control measures of COVID-19,and taking into account household clustering,we put forward a household model based on a bipartite metapopulation network to assess the impact of quarantine and medical resource on transmission.The main research contents and innovation points are as follows:?1?We derive moment-closure metapopulation network models and give dynamiclal analysis.The moment-closure model with two-dimensional one-point distribution is equivalent to the heterogeneous mean field model.For this moment-closure model,the basic regeneration number is calculated,and the global stability of the disease-free equilibrium and endemic equilibrium is proved.Numerical simulation shows that there is an endemic equilibrium for the moment-closure model with two-dimensional lognormal distribution.By comparing the numerical simulation with the stochastic simulation,it is found that the model we derived optimizes and generalizes the heterogenrous mean-field model.It is also found that the higher the mobility rate is,the faster the transmission spreed is in a large scale,but the mobility rate has no effect on the steady state of infections.?2?We give dynamical analysis of a metapopulation network model under the human muti-step mobility mode.This paper definesd^th?32?neighbors and d^th?32?-neighbor networks,builds a dynamical model of infectious diseases based on a metapopulation network coupled with its second neighbor,obtains the explicit expression of the basic reproduction number which is independent of the mobility mode,and proves the global stability of disease-free equilibrium and endemic equilibrium.It is found that moderate transfer rate is conducive to the large-scale spread of infectious diseases.?3?We give dynamical analysis of an adaptive metapopulation network model under two-way travel restrictions.This paper defines an adaptive metapopulation network based on the relative infection density of infectious individuals in subpopulation and intervention time for two-way travel restrictions,and calculates the basic regeneration number,and the final size under special circumstances.Comparing one-way travel restrictions and two-way travel restrictions,we find that controlling the movement of infectious individuals helps prevent the global spread of infectious diseases and adaptive metapopulation networks under two-way travel restriction are most most helpful in curbing the global spread of diseases.In addition,the heterogeneity of network structures promotes the global spread of disease.?4?We apply a household model coupling quarantine and medical resources under a metapopulation network to COVID-19 transmission in Wuhan city.The model predicts that the final size of Wuhan city is 50,662?95%CI:46,234,55,493?,and that the epidemic will last until April 25?95%CI:April 23,April 29?.It is found that about 87 percent of Wuhan residents will eventually be infected if close contacts are not quarantined;fully centralized quarantine of close contacts could reduce the final size by about 7,000 from January 23 with existing containment measures;the opening of module hospitals could reduce the final size by about 17,000 and shorten the epidemic duration by ten days.It is alos found that deviding a household into multiple smaller size household can effectively reduce the final size.To some extent,it also reflects that closing high-concentration places such as entertainment places is conducive to the control of the epidemic.