Analysis Of Disease And Information Spreading On Overlay Network

Epidemical dynamic on networks is a main branch of biological dynamics.In this branch,on the basis of the propagation mechanism of epidemics on networks,one can build the network-based epidemical models and further analyze their dynamical behaviors.Then,according to these results obtained,the epidemical prevalence can be predicted and then early-warning can be made,which reduces injures diseases give people.In real world,disease and the relevant information about it spread concurrently.When one gets the disease information,he or she will protect himself or herself by some ways from being infected.In other words,this individual getting information becomes vigilant for the disease.Meanwhile,when an infected individual recovers,he or she may be vigilant for the disease.Therefore,this paper studies epidemical dynamic models of disease and information about disease spreading on overlay network.Chapter 1,describes the impacts of infectious disease on the public life and indicates the significance of studying epidemical dynamical models.Then,it presents synopsis of the current state of this kind of model research.Finally,the main contents and methods used in this paper are given.Chapter 2,establishes an SAIS model on a two-layer overlay network,in which both layers are undirected.Then,using the Taylor's formula and Matrix theory,the second threshold of infection strength is obtained.Furthermore,it is also found through numerical simulations that the alertness of recovery increases the second epidemic threshold of infection strength and also effectively reduces the infection size.In other words,the dissemination of disease information inhibits the epidemic spreading.Chapter 3,considers a double-layer network.The bottom layer is an undirected networks,called the contact layer in which disease and information spread by infected individuals and contacts made by them with non-infected individuals;The upper layer is a directed network,called information layer where the information spread by virtually contacting with infected persons(such as virtual phone,WeChat,Facebook,etc.).Then,we establish a new SAIS model on directed network.Furthermore,by using the Taylor's formula and Matrix theory,the expression of the second threshold of infection strength is obtained.Finally,the main results obtained in this chapter are verified by numerical simulation.Chapter 4,summarizes the core ideas of this paper and proposes some ideas for future research.