On Two Classes Of Epidemic Models With Media Coverage

In real life,the spread of infectious diseases endangers human health,and there is also a long history of the study of infectious disease models.In recent years,more and more scholars have taken into account the impact of media coverage on the transmission of infectious diseases,and there are also a lot of research results[1,2]on the infectious disease models coverage by the media.However,in the process of infectious disease transmission in real life,they are affected by other factors,such as temperature and so on.Therefore,this paper considers the influence of environmental noise interference on infectious diseases.Also,the contact between people is limited in the process of disease transmission,so the influence of saturation incidence on disease is also considered in this paper.Main content As followsFirst,the following deterministic SIS epidemic model incorporating media cover-age and saturated incidence is established.Firstly,the existence of the disease-free equilibrium point and local equilibrium point of deterministic model is discussed,and then the global asymptotic stability of a deterministic model is discussed by using the Lyapunov function,LaSalle invariant set principle,the Routh-Hurwitz criterion and so on.Considering the interference of random factors in an epidemic,we establish the following stochastic SIS epidemic model incorporating media coverage and saturated incidence.By constructing the Lyapunov function and the formula of Ito shows that the stochastic model has a global unique positive solution.On this basis,two sufficient conditions for disease extinction and one sufficient condition for disease persistence are given and verified by using numerical simulations.Second,Considering some diseases,patients may be directly infected again after treatment and recovery.A random SIRI epidemic model with media coverage and saturation incidence is established.In this paper,we first consider the existence of the equilibrium point of the stochastic model corresponding to the deterministic model,then we prove that the stochastic model has a globally unique positive solution and study the upper and lower oscillatory behavior of the solution of the stochastic model around the equilibrium point of the corresponding determined model,and then give a sufficient condition for the persistence of the disease mean value of the stochastic model.Finally,the numerical simulation verified the above results.