Dynamic Studies Of Several Types Of Cholera Infectious Disease Models Based On Spatial Diffusion

With the spread of cholera epidemic as the main background,this paper mainly studied three types of cholera models: the reaction-diffusion cholera model with nonlocal delay,the reaction-diffusion cholera model with age-structure,and the reactiondiffusion cholera model with periodicity.The nonlocal time delay,periodicity and age-structure caused by the fixed incubation period were considered comprehensively,which made the established model more complex compared with the previous models and enriched the research content of cholera infectious disease transmission.At first,considering the spatial heterogeneity and incubation period of infection,we deduced with nonlocal delay reaction diffusion model of cholera,and further analyzed the dynamic of the above model.By using the classical dynamics analysis method,we solved some key problems including the basic reproductive number problem,the principal eigenvalue problem and the threshold dynamics,and studied the impact of these indicators on the spread of infectious diseases,which were important contents of infectious diseases dynamics;Thirdly,by adding age-structure factors,we deduced a diffusion reflecting model and two Volterra integral equations,and obtained two constant equilibria,and defined the basic regeneration number that determines the persistence and extinction of the disease,and studied the local stability,consistent persistence and global attraction of the equilibrium.Finally,we considered the periodicity of cholera,and given the suitability of the model,defined the basic regeneration number,and studied its threshold dynamics.