Kinetic Studies Of Two Classes Of Epidemic Models With Beddington-DeAngelis And Crowley-Martin Incidence

Infectious diseases are the biggest enemy of human life,and the struggle between human beings and infectious diseases has continued to this day.Since the outbreak of coronavirus in December 2019,the prevention and control of infectious diseases has become a major focus of global human attention.Aiming at the spread and prevention of various infectious diseases,researchers study the spread and prevention of infectious diseases by establishing differential equation mathematical model,so as to control the spread of diseasesThis paper mainly studies two kinds of SIR epidemic models with BeddingtonDeAngelis incidence and Crowley-Martin incidence.Firstly,we consider the SIR epidemic model of the deterministic system with Beddington-DeAngelis incidence.By constructing an appropriate Lyapunov function and according to the Lyapunov-LaSalle invariant set principle,we prove the global stability of the disease-free equilibrium point and the global stability of the endemic equilibrium point of the SIR epidemic model with Beddington-DeAngelis incidence,Finally,the correctness of the conclusion is tested by MATLAB.Then we study the dynamic behavior of stochastic SIR epidemic model with Crowley-Martin incidence considering natural recovery.By constructing an appropriate Lyapunov function and applying It(?) formula,we prove the existence of the globally unique positive solution of the model,and prove that in the stochastic SIR infectious disease model,when the basic regeneration number R*?1 or the random disturbance is large enough,the disease will tend to extinction.When the basic regeneration number R*>1,the disease will persist.Finally,we verify the accuracy of the results through MATLABThis article is mainly divided into the following four parts:The first part mainly expounds the development background of infectious diseases and the practical research significance of infectious diseasesIn the second part,we mainly give the concept of parameters in the study of infectious disease dynamics and their biological significance in the study of infectious disease dynamics,and give the relevant judgment theoremsIn the third part,we mainly consider a SIR epidemic model of a certain system with Beddington-DeAngelis incidence.We prove the global asymptotic stability at the equilibrium point by constructing an appropriate Lyapunov function,and prove the accuracy of the conclusion by numerical simulationIn the fourth part,we consider a class of stochastic SIR infectious disease model with Crowley-Martin incidence.On the basis of determining the system,we introduce random disturbance to establish the stochastic infectious disease model.By constructing Lyapunov function and applying It(?) formula,we prove that the system has only one positive solution and obtain the conditions of disease persistence and extinction,The accuracy of the conclusion is proved by numerical simulation...