Study On Threshold Dynamics Of Reaction-diffusion Cholera Model With Seasonality And Different Infectivit

Cholera is a water-borne infectious disease caused by Vibrio cholerae,which has caused extremely serious impacts on countries such as South Africa(2000-2001),Angola(2006),Zimbabwe(2008-2009),and it has became a endemic disease in many countries.The outbreak of cholera is a threat to global public health and one of the key factors affecting social development.In order to study the transmission of cholera and analyze the corresponding control strategies,as well as to explore the impact of seasonal induction incubation period,high bacterial infectivity and spatial heterogeneity on the spatiotemporal transmission dynamics of cholera,this dissertation constructed a diffusive cholera model with seasonal incubation period and Neumann boundary conditions,our purpose is to study the threshold dynamics based on the basic reproduction number R0.If R0<1,then the disease-free steadystate is globally attractive,which means that the cholera will extinct;If R0>1,then the system is persistent and admits at least one positive steady state,this means that the cholera endemic happens.In the case of space homogeneity,the global attractivity of the unique constant endemic equilibrium is verified by constructing the Lyapunov functional.