Control Study On A Class Of Stochastic SIRS Epidemic Model With Information Intervention

When infectious disease outbreak,related media coverage and drug therapy are effective way to curb the spread of disease.Thus,media coverage and/or drug therapy have been introduced into the classical compartment model to study the dynamics behavior of disease.Meanwhile,the environ-mental noise also is an significate factor to influence the spread of disease.Therefore,we introduce some factors into the model proposed by Kumar et al.[J.Theor.Biol.,414:103-119,2017],and study related properties of model in this paper.The details are as follows:(i)A deterministic infectious model with treatment and information intervention is studied.We calculate the two equilibrium points:the disease-free equilibrium E0 and endemic equilibrium E*.The local asymptotic stability of the two equilibriums are investigated,which indicates that the basic reproduction number R0 can govern the extinction and persistence of disease.Finally,some numerical examples are presented to illustrated the effectiveness of theoretical results.In addition,we provide the sensitivity analysis of RO to the intensity of treatment m2.(ii)We study the dynamics behavior of a stochastic SIRS model with information intervention in this part.We find that the stochastic basic reproduction number Ros can be a threshold of model:when R0s<1 under a mild condition,the solution of the stochastic model will goes to the disease free equilibrium of the corresponding deterministic model with probability one,which means the extinction of disease;when R0s>1 without any other condition,there exists a stationary distribution for stochastic model,which implies the disease is prevalent.Finally,we illustrate the effectiveness of theoretical results by some numerical simulation.