Dynamic Analysis Of Three Classes Of Epidemic Models

Infectious diseases are diseases caused by pathogenic microorganisms and par-asites that can be transmitted from person to person,animal to animal or between people.It not only threatens the survival of human beings,it even poses serious challenges to the development of the world.Based on the research status of infec-tious disease control,treatment and prevention,this paper constructs several types of mathematical models.Through the dynamic analysis of infectious disease models,it reveals its epidemic rules,predicts development trends,and provides theoretical foundations for people's prevention and treatment decisions.The qualitative and stability theory of ordinary differential equations is used to study the epidemic mod-el with Holling III type treatment rate and public health education and saturation treatment rate.Using the stability theory of fractional differential equations,the fractional SIRS with time delay the dynamic behavior of the model is studied.This article is divided into five parts.The first chapter introduces the background of infectious diseases and the status of mathematical research.In the second chapter,based on the effect of treatment on the spread of cholera,a class of cholera model with Holling III type treatment function is studied.Based on the second additive composite matrix theory,lyapunov stability theory,central manifold theory,etc,the system is discussed.The stability and branching problems are given,and new thresholds for controlling disease elimination are given.Finally,numerical simulations verify the correctness of the conclusion.The third chapter considers the impact of a class of public health education and treatment on controlling the spread of disease,and constructs a class of infectious disease models with public health education and saturation treatment rate.First,the basic regeneration number is given using the regeneration matrix method.The expression of R₀.Second,the local and global stability of the equilibrium point are discussed by the eigenroot method.Finally,the numerical analysis is used to verify the correctness of the theoretical analysis.In the fourth chapter,based on the stability theory of fractional differential equations,discusses a class of fractional SIRS epidemic models with time delays.The stability and branching of the system are studied.The time delay?is selected as the branch parameter.The characteristic root method discusses the local stability and branching of the equilibrium point.Finally,the numerical analysis is used to verify the correctness of the theoretical analysis.The fifth Chapter summarizes the rearch work of this dissertation and looks forward to future work.