Time And Space Dynamics Analysis Of Several Types Of Vector Infectious Disease Models

Taking malaria infectious disease transmission as the main background,this paper mainly studies three types of malaria models: reaction-diffusion malaria model with non-local delay,malaria model with vector selectivity and periodicity,and non-local delay,vector selectivity and Periodic reaction-diffusion malaria model.Considering the non-local time delay caused by fixed latency,periodicity and bias selection of media,and other factors,and in the model of this paper,it is assumed that the susceptible population is constant,making the Compared with previous models,the model is more complex and enriches the research content of malaria infectious disease transmission.In different state spaces,the dynamic analysis of the above model will involve the basic regeneration number problem of the reaction-diffusion infectious disease model,the main eigenvalue problem and the threshold dynamics and other key issues,using classic dynamic analysis methods,Analyzing the impact of these indicators on the spread of infectious diseases is an important part of infectious disease dynamics research.Taking the above factors into our vector-borne infectious disease model will bring some new challenges,such as: the well-posedness analysis of the model,the existence of the global attractor and the threshold dynamics of the basic regeneration number.This paper wants To solve these problems,some analysis skills need to be combined,for example: The linearization method and eigenvalue theory are used to study the stability of the equilibrium state.The consistent continuity theory of the infinite dimensional dynamic system proves that the system is always continuous under the threshold.The theory defines the spectral radius of the regeneration operator as the basic regeneration number,etc.The dynamics results of the model analysis can be used to describe the disease transmission trend.