一类具有非线性发生率的随机SIS传染病模型阈值动力学行为研究

Threshold Dynamical Behaviors of a Stochastic SIS Epidemic Model with Nonlinear Incidence Rate

考虑到环境波动对传染病传播过程的影响,该文研究了一类具有非线性发生率的SIS随机传染病动力学模型的阈值动力学行为.利用Feller检测和随机比较原理得到了决定疾病绝灭或持久的随机基本再生数R_0~s,即当R_0~s<1时,疾病将趋于绝灭;当R_0~s=1时,疾病也将趋于绝灭,这一结论补充了已有随机阈值结果;当R_0~s>1时,疾病将随机持续下去,并给出了最终传染规模的范围估计.最后,利用数值仿真验证了文中所得出的结论并根据实际生物参数说明了环境波动对不同大小尺度群体中SIS传染病传播的影响.

In this paper, a stochastic susceptible-infected-susceptible （SIS） epidemic model with nonlinear incidence rate is considered to investigate the effect of environment fluctuation on the transmission threshold dynamical behaviors. By using Feller＇s test and stochastic con〉 parison principle, we obtain the stochastic basic reproduction number RO^S, which determined whether the disease persistent or not. If RO^S〈 1, the disease will go to extinction. If RO^S= 1, the disease will also go to extinction in probability, which has not been reported in the known literatures. In addition, if RO^S〉 1, the disease will stochastic persistence and the scale range estimation of spread is presented eventually. Finally, numerical simulations are carried out to support the theoretical results. According to the actual parameter, it illustrated the environ- mental fluctuation have different effect on different size of group.