Study On The Traveling Wave And Turing Pattern Of Epidemic Model On Metapopulation Networks

At present,the outbreak of infectious diseases infected by individual exposure poses a serious threat to public health.In recent years,the development of the metapopulation epidemic dynamics has provided a good way to study the spatial spread of infectious diseases.On the one hand,the metapopulation network epidemic model is more specific in describing infectious diseases.On the other hand,the spatial distribution characteristics of infectious diseases are considered in the model,which makes the model more suitable for the actual situation.Using the metapopulation epidemic model to understand the spread law of infectious diseases among metapopulations(or patchs),to find out its transmission mechanism,and to propose reasonable preventive and control measures have become a problem that cannot be underestimated.In this paper,we mainly studied the traveling wave solution of a metapopulation epidemic model on a regular tree network and Turing patterns of metapopulation epidemic model with non-local diffusion on complex network.This paper is mainly divided into four parts.In chapter 1,we mainly give the research background of the metapopulation epidemic model,the development process of traveling wave solution of metapopulation epidemic model on the lattice dynamic system and Turing pattern on complex networks,as well as the research status at home and abroad,and introduce the main work of this paper.In chapter 2,we propose an metapopulation epidemic model on the regular tree network with two kinds of boundary conditions.Under two kinds of boundary conditions,the existence and nonexistence of traveling wave solutions of the model are obtained.In addition,some properties of traveling wave solutions of the model are studied.In chapter 3,we propose a SIS network epidemic model of metapopulation with non-local diffusion.Firstly,we explore the threshold of the positive equilibrium point,the stability of the positive equilibrium point and the type of singularity without considering diffusion.Then,we introduce the non-local diffusion into the model and explore the condition of Turing instability.Finally,we carry out numerical simulations on different metapopulation networks to explore the formation of Turing pattern.In Chapter 4,Summarize the main conclusion of this paper and look forward to the future development.