具有标准发生率的脉冲随机SIS传染病模型的动力学分析

Dynamics analysis of an impulsive stochastic SIS epidemic model with standard incidence

同时考虑随机干扰、生育脉冲和脉冲治疗,建立一类带有标准发生率的SIS传染病模型.利用随机微分方程理论,得到了平凡解随机稳定的充分条件;利用离散映射,得到无病解存在的充分条件;利用伊藤公式证明了疾病的随机灭绝性.此外,还通过数值模拟验证理论分析的结果.

Random disturbance,birth pulse and pulse treatments were simultaneously considered to build a class of SIS epidemic model with standard incidence.By applying the theory of stochastic differential equation,the sufficient conditions for the stochastic stability of the trivial solution were obtained.The sufficient conditions for the existence of the disease free solution were obtained by using a discrete map.The stochastic extinction of the disease was investigated by using the It formula.Moreover,numerical simulation was conducted to verify the theoretical analysis.