Modeling And Analyzing On Two Classes Of Immuno-epidemiological

Malaria is a mosquito-borne disease transmitted from person to person by anopheles mosquitoes,At present,not only there is lack of effective vaccines,but also the rule of the disease transmission dynamics is still not fully be understood.In addition,typhoid fever,cholera and other diseases are caused by people's exposure to water and food contaminated by bacteria,and their outbreaks and epidemics brought serious threat to human life and health.Today these diseases are listed by the World Health Organization as important infectious diseases.According to the transmission characteristics of malaria,typhoid fever and other diseases,by using the theories and methods of epidemiology and dynamic system,in this dissertation,we establish and analyze two classes of immune-epidemic disease dynamical models.?1?According to the characteristics of malaria infection and transmission in hu-man population and the immune status of host population,the vector-host epidemic dynamics model is established by using ordinary differential equation?ODEs?and partial differential equation?PDEs?with size and structure.By the basic reproduc-tive number theory of epidemic disease,the operator characteristic equation theory and by applying the persistence theory for infinite-dimensional systems.The dis-ease reproductive number to control malaria transmission was obtained,the dynam-ic characteristics of disease transmission were analyzed,the sustainable survival of malaria epidemic was obtained,and the existence of multiple endemic equilibriums and the phenonmenon of backward branch of disease transmission were explained and analyzed.?2?Combined with the process of cholera infection,bacteria and immune cell dynamics within host and dynamics of controlling the spread of disease between host population,we construct a class of immuno-epidemiological model with multiple scale.By using the theory of the stability and persistence of the infinite dimensional dynamical system and methods of constructing Lyapunov function,the existence of the equilibria,the stability and persistence of disease are analyzed,the threshold condition for controling the transmission of disease is obtained.When the threshold condition R₀<1,disease-free equilibrium is global asymptotically stable.When R₀>1,the endemic equilibrium is global asymptotic stability.The effects of viral epidemic in host on the spread of disease among human populations is analyzed by numerical simulations.