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A detailed analysis was carried out on global asymptotic behavior of a kind of stochastic SIRS(susceptible-infective-removed-susceptible)model.This model has been obtained by introducing stochasticity into the original deterministic SIRS model via the technique of parameter perturbation which is standard in stochastic population modeling.By making corresponding Lyapunov function and using It formula,the condition for the solution of the model tending to the disease free equilibrium asymptotically was obtained.Under this condition,the epidemics will die out as time goes by.Based on this,almost surely exponential stability was analyzed.
A detailed analysis was carried out on global asymptotic behavior of a kind of stochastic SIRS (susceptible-infective-removed-susceptible) model. This model has been obtained by introducing stochasticity into the original deterministic SIRS model via the technique of parameter perturbation which is standard in stochastic population modeling.By making corresponding Lyapunov function and using It formula, the condition for the solution of the model tending to the disease free equilibrium asymptotically was obtained. Under this this, the epidemics will die out as time goes by. Based on this, almost surely exponential stability was analyzed.