Stability Study Of Two Classes Of Infectious Disease Models With Vertical Contagion And Age Structure

The infectious diseases are a kind of diseases caused by various pathogens that can spread between people,animals and animals,or between people and animals.The main modes of transmis-sion are contact infection,vertical infection,fecal infection and so on.The emergence and spread of infectious diseases have brought serious threats to the survival and development of human beings,so how to effectively reveal the epidemic law of infectious diseases has become an urgent subject for people to study.By studying the dynamic state of the established mathematical model,we can reveal the process of disease development,predict its epidemic law and development trend,and achieve the purpose of prevention and control.This paper mainly studies the stability of two classes of infectious models with vertical and age structure.In the first chapter,we introduce the background and significance of the topic selection.The research status of the infectious disease model with vertical infection and the age structure infectious disease model are described.In the second chapter,the existence and uniqueness of the non-negative solution of the system are proved by using the fixed point theorem.The existence of the disease-free equilibrium point is proved by normalization.The expression of the basic reproduction number R0 is obtained by using the characteristic equation.It is proved that when R0<1,the disease-free equilibrium is locally asymptotically stable,and when R0>1,the disease-free equilibrium is unstable.In the third chapter,based on the theory of differential equation,the sufficient condition of equilibrium point is proved,and the expression of basic regeneration number R0(?)is obtained.We prove that the disease-free equilibrium is locally asymptotically stable at R0(?)<1 and globally asymptotically stable at R0(0)>1 and ?2=0.