ON THE THRESHOLD DYNAMICS OF THE STOCHASTIC SIRS EPIDEMIC MODEL USING ADEQUATE STOPPING TIMES

摘要

As it is well known, the dynamics of the stochastic SIRS epidemic model with mass action is governed by a threshold R_s- If R_s ＜ 1 the disease dies out from the population, while if R_s ＞ 1 the disease persists. However, when R_s = 1, classical techniques used to study the asymptotic behaviour do not work any more. In this paper, we give answer to this open problem by using a new approach involving some adequate stopping times. Our results show that if R_s = 1 then, small noises promote extinction while the large one promote persistence. So, it is exactly the opposite role of the noises in case when R_s ≠ 1.