Effect Of Noise On A Stochastic Infectious Disease Model With Crowley-Martin Incidence And Isolation Term

Infectious disease is a class of important disease endangering human health,and a serious problem affecting public health security.In recent years,human beings have been struggling with COVID-19,which has led to a greater focus on research on infectious disease issues.By establishing a reasonable mathematical model of the transmission pattern of infectious diseases,to describe the process by which infectious disease spreads,we can study the speed of transmission and the final size of infectious diseases,finally we can provide effective prevention and control strategy.In this thesis,we mainly consider a class of stochastic SIQR infectious disease models with Crowley-Martin incidence rate.Firstly,we consider the SIQR deterministic infectious disease model with vaccination and quarantine terms,give the basic reproduction number of the deterministic system,and prove that disease-free equilibrium E0 is globally asymptotically stable when the basic reproduction number R0≤1,endemic equilibrium E*is globally asymptotically stable when the basic reproduction number R0>1.Secondly,for the stochastic SIQR infectious disease model with Crowley-Martin nonlinear incidence rate,the existence of a globally unique positive solution for the stochastic system is proved through the Lyapunov function and the It?’s formula,and the threshold value R*of the stochastic infectious disease model is given,we obtain the sufficient conditions for the extinction and persistence of the disease in the stochastic system.Finally,in this thesis,a series of numerical simulations are carried out to verify the correctness of the theory.