Study On Two Epidemic Models On A Dynamic Contact Network Of Mobile Individuals With Spatial Constraints

The spread of infectious diseases is one of the most urgent issues in the world.It is of great significance to study the the spread of infectious diseases and to devise effective strategies for control and containment.Mathematical modeling is an effectual tool to study the spread of infectious diseases.Network-based epidemic models have been extensively employed to understand the spread of infectious diseases,but have generally overlooked the fact that most realistic networks are dynamical rather than static and the activity sphere of individuals axe constrained in terms of spatial distances.Moreover,the limitation of individuals on the spatial distance will lead to the localization of contacts between individuals,which will in turn affect the transmission of infectious diseases throughout the underlying contact network.To address this issue,in this paper,we propose a susceptible-infected-susceptible(SIS)model and susceptible-infected-susceptible epidemic model with vaccination(SIV)model in a dynamical contact network of mobile individuals with spatial constraints.The main contents are as follows:The first chapter introduces the purpose and significance of our research and the current research status of relevant topics at home and abroad.In addition,main works in this paper are provided.The second chapter gives the basic concepts of network and the structure of random walk model,further giving a SIS model on random walk network.The third chapter mainly propose an SIS epidemic model on a dynamical network based on random walks.We assume that both susceptibilities and interaction radii among individuals are heterogeneous on the epidemic dynamics.The basic reproduction number R0 and the global stability of the disease-free equilibrium and the endemic equilibrium are given.It is found that the susceptibilities and interaction radii have important effects on the basic reproduction number.The forth chapter describes an SIV model on a dynamical contact network of moving individuals with spatial constraints.We consider the scenario where the individuals have a heterogeneous probability distribution of interaction radius and infected individuals are vaccinated with a probability that depends on the interaction radius and its distribution.We derive the basic reproduction number R0 and carry out the stability analysis of equilibria.It is found that R0 and the final density of infected individuals are strongly related to the interaction radius distribution.In particular,it is proportional to the second order moment of interaction radius<r2>in the special case of a constant vaccination rate.This study provides potential implications for developing efficient containment measures against infectious disease according to the spatial constraints of individuals.In Chapter 5,we summarize the main conclusions of this paper and point out some problems to be solved for future research.