Study On Two Infectious Disease Models Based On Complex Network

Infectious diseases not only harm human bodies,but also may bring disasters to society.For some multi-stage diseases with a long infection period,such as tuberculosis and rubella,those infected individuals often have different infectivity at different stages.Different transmissibilities have different effects on the spread of disease.On the other hand,the contact structure of the pop-ulation also affects the spread of disease.The traditional compartment model ignores the impact of the contact structure of the population on the spread of disease.In this paper,considering the multi-stage of the disease and the contact structure of the individual,we establish two progression models based on complex networks.We study the dynamic behaviors of models.The threshold conditions of various models are obtained,and the stabilities of equilibrium are analyzed.In addi-tion,the impacts of the staged structure of the disease and the contact mechanisms of individuals on disease transmission are discussed.In chapter 2,We establish an infectious disease model with birth and death in the regular network.Since some diseases will experience two stages:mild and severe stages,those infected individuals in different stages have different infectivity,and the susceptible individuals enter two different infection stages in a certain proportion（p or 1-p）after they are infected.Therefore,we establish an infectious disease model with two stages,mild and severe.We analyze the impact of different stages of infectious diseases on the dynamics of infectious disease.The basic reproduc-tion number₀of the model is calculated.We prove that the disease-free equilibrium is globally asymptotically stable when₀<1.When₀>1,the disease-free equilibrium is unstable.The global stability of the endemic equilibrium is verified by numerical simulations,and the impact of the parameteron the basic reproduction number₀and the density of infected individuals in different stages is further analyzed.In chapter 3,the mean-field method is used to establish a dynamic model of SIS epidemic transmission based on weak clustering network.We calculate the basic reproduction number₀.Furthermore,by constructing Lyapunov function,we prove that the disease-free equilibrium of the model is globally asymptotically stable when₀<1.When₀>1,there is only one positive equilibrium which is globally asymptotically stable.In random network and scale-free network,the influence of clustering coefficient on the spread of infectious diseases is analyzed by numerical simulations.The results show that the infection proportion and the basic reproduction number₀increases as the clustering coefficient increases when the average degree of networks is fixed.