Dynamics Analysis Of Multigroup Epidemic Models With Stochastic Perturbations

People have always been quite concerned about infectious diseases.From the past to the present,the struggle between human beings and infectious diseases has never stopped.The threat posed by infectious diseases to mankind and society cannot be ignored,and it is therefore important to study the transmission patterns of infectious diseases.Modeling the epidemic law and development trend of infectious diseases by mathematical methods has been widely concerned by the society.However,the main consideration is the deterministic model,which is difficult to describe the interference effect of random factors in the spread of infectious diseases,so the study of stochastic epidemic models is more practical significance.As the dynamics of infectious diseases continue to be studied in depth,more and more factors are being taken into account in mathematical modelling.For example,it is often necessary to construct multigroup epidemic models to characterise more complex infectious disease transmission scenarios due to the age,gender and geographic location of the infected host.This is also a hot issue in current research.The second part constructs a stochastic multigroup SIS model,and based on this model,the epidemic model with saturated incidence rate is considered.Firstly,the existence and uniqueness of global positive solutions are analyzed.Secondly,it is proved that the system has a unique stationary distribution,which indicates the persistence of the disease.Furthermore,the sufficient conditions for disease extinction are obtained by constructing suitable Lyapunov functions.The results show that the condition of disease extinction in stochastic system is weaker than that in deterministic system.In the third part,a multigroup SIS epidemic model with limited medical resources is established,and the dynamics of deterministic model and stochastic model are analyzed.For the deterministic model,the global asymptotic stability of the disease-free equilibrium and the uniform persistence of the disease are proved.Then,the dynamic behavior of the stochastic model is studied,and the existence and uniqueness of the global positive solution of the system and the asymptotic stability of the disease-free equilibrium point are proved,and the asymptotic behavior near the endemic equilibrium is analyzed.The results show that providing patients with timely and efficient treatment and investing more medical resources can effectively control the spread of the disease.