A Study On Coupled Dynamic Models Of Disease And Awareness Spreading On Multiplex Networks

The study of disease spread dynamic models has long been one of the hottest research topics at home and abroad,although it can date back to over a hundred ago.With the continuous deepening understanding about epidemic transmission,recently more and more researchers turn to employ high-dimensional network-based transmission models rather than the classic low-dimensional compartmental transmission models.However,most existing studies on disease transmission on complex networks focus on the models consisting of one-layer network and one type of transmission process.These studies have largely neglected an important fact:the epidemic outbreak often leads to the diffusion of related information,panics,self-protective awareness and opinion about disease,through various routes.These behavior will in turn affect the contact pattern in the population and influence the disease spread process,which in essence comes down to the issue of coupled dynamics of disease transmission and awareness diffusion on multiplex networks.To this end,this thesis studies two coupled dynamics models of disease and awareness spreading on multiplex networks and investigates how the awareness diffusion influences the disease transmission dynamics from different perspectives.This thesis contains four chapters as follows.In chapter one,we present the background and significance of our research,and outline the main contents and ideas for the study.In chapter two,we study a coupled dynamic models for disease transmission and awareness diffusion with nonsynchronous updating on multiplex networks.The basic reproduction number of the model is calculated,and the dynamic equation under continuous time is given.Through stochastic simulations,it is found that the two kinds of asynchronous updating order,i.e.“disease prior to awareness” and “awareness prior to disease”,have different effects on disease transmission.The asynchronous updating order of “information prior to disease” is more favorable for controlling the disease outbreak.In chapter three,we propose an effective degree model for disease transmission and awareness diffusion on multiplex networks,taking into account the effect of awareness-dependent adaptive link rewiring on network structure and disease spread.By employing the next generation matrix method,we analyze the basic reproduction numbers both for disease transmission and awareness spread,and obtained the lower bounds for these numbers.It is shown that individuals’ adaptive rewiring behavior will lower the basic reproduction number for disease transmission,thus helping restraining the epidemic.Moreover,our results demonstrate that there is a critical phenomenon in the relationship between the disease outbreak threshold and the awareness diffusion rate.For relatively small values of the awareness diffusion rate,the disease outbreak threshold keeps unchanged with the change of the awareness diffusion rate.However,once the awareness diffusion rate exceeds a certain critical value,the disease outbreak threshold increases monotonically with the awareness diffusion rate.All these results indicate that the awareness diffusion process and individuals’ behavior of adaptive link rewiring play an important role in containing the disease transmission.In chapter four,we summarize this paper and discuss some relevant issues for future research.