Stability Analysis Of A Reaction-Diffusion Host-Pathogen Model With Periodic Delay

In all ages,human health is always the important problem of social concern.Infectious diseases are the main factors endangering human health.Infectious disease prevention and eradication is a global issue that each country must face.It is a hot issue to study the spread risk of infectious diseases and evaluate the effectiveness and timeliness of prevention and control strategies by using infectious disease dynamics model.The purpose of this dissertation is to establish appropriate mathematical model,so as to better understand the transmission mechanism of infectious diseases.The goal of this dissertation is in order to discuss:(i)Global dynamics analysis for a reaction diffusion cholera model with a nonlocal delay with seasonal intrinsic latency;(ii)Global dynamics analysis for a reaction diffusion malaria model with a nonlocal delay with seasonal external latency.Both cholera and malaria models take into account periodicity,spatial heterogeneity,seasonally forced incubation period and nonlocal delay.In particular,the malaria model introduces a vector-bias selection mechanism for mosquito bites.Both models first analyze the suitability,then define the basic reproduction number,and the transmission trend of cholera and malaria is analyzed by taking it as the threshold value.In particular,by constructing the Lyapunov function,we prove the global attractivity of the positive equilibrium in the case of spatial homogeneity of the cholera model.The findings demonstrate that the disease–free periodic solutions of the two models are global attractive when the basic reproduction number is smaller than 1.Both cholera and malaria infections diseases persist when the basic reproduction number is greater than 1.The model analysis in this paper is also applicable to other similar reaction diffusion epidemic models with a nonlocal delay with seasonally induced latency.