一类具有隔离效应的随机SIS传染病系统的动力学行为

The dynamic behavior of a class stochastic SIS epidemic system with quarantine effect

研究了具有饱和发生率和隔离效应的随机SIS(Susceptible Infective Susceptible)传染病模型的动力学行为.首先,给出具有任意正初值的随机系统全局正解存在的唯一性.其次,当R0<1,白噪声强度较小时,通过构造合适的Lyapunov函数,得出随机系统在确定性系统无病平衡点附近的渐进行为,说明疾病在此条件下将灭绝;当R0>1,且满足一定条件时,利用Hasminskii遍历理论得出随机系统存在遍历的平稳分布,这意味着疾病将持久流行.所得结果表明,环境白噪声对传统病系统的阈值具有重要影响.

The dynamic behavior of infectious disease model of randomized SIS（Susceptible Infective Susceptible）with isolation and saturation rates was studied.Firstly,the existence of global positive solutions for random systems with arbitrary positive initial values is given.Then,when R0〈1 and the white noise intensity is small,the appropriate Lyapunov function is constructed to obtain the asymptotic behavior of the stochastic system near the disease-free equilibrium point,indicating that the disease will be extinct under this condition.When R0〉1 and satisfying certain conditions,the use of Hasminskii ergodicity theory yields a ergodic steady distribution of the stochastic system which means that the disease will persist.The results show that the environment white noise has an important effect on the threshold of the infectious disease system.