具有信息干预的随机SIRS模型的平稳分布和灭绝性

Stationary distribution and extinction of a stochastic SIRS model with information intervention

提出一个带有信息干预和环境噪声影响的SIRS流行病模型.给出了可以作为流行病持久和灭绝阈值的随机基本再生数R_s.当噪声强度很大时,R_s<1流行病将会灭绝;当噪声强度很小时,R_s> 1并得到了平稳分布存在的充分条件,即流行病将会持久.研究结果表明信息干预和白噪声对疾病有很大的影响.通过数值模拟验证了主要结果.

An SIRS epidemic model which considers the influence of information intervention and environmental noise is studied in this paper. We prove that the stochastic basic production is a threshold which determines the extinction or persistence of thedisease. When the intensity of noise is large, we obtain that the disease will die out. When the intensity of noise is small, a sufficientcondition for the existence of stationary distribution is obtained, which means that the disease is prevalent. The study shows that information intervention and white noise have great effects on the disease. The main results are illustrated by numerical simulations.