Dynamics of a novel nonlinear stochastic SIS epidemic model with double epidemic hypothesis
Dynamics of a novel nonlinear stochastic SIS epidemic model with double epidemic hypothesis
复制标题
具有双重流行假设的新型非线性随机 SIS 流行病模型的动力学
DOI：
10.1016/j.jmaa.2015.07.056
复制
发表时间：
2016-01-01
影响因子：
1.3
通讯作者：
Zhang, Tonghua
中科院分区：
文献类型：
--
作者：
Meng, Xinzhu;Zhao, Shengnan;Zhang, Tonghua
本文提出了具有非线性发病率和双重流行病假设的新的数学模型。然后，我们致力于发展一种方法来获得的阈值的随机SIS流行病模型。为此，首先，我们研究了确定性系统平衡点的稳定性，得到了两种传染病绝灭和持续生存的条件。其次，我们研究并得到了一类随机SIS系统的灭绝阈值和两种传染病平均持续生存的阈值。结果表明，一个大的随机扰动可以使传染病走向灭绝，换句话说，一个确定性系统的持续性传染病可以由于白色噪声随机扰动而走向灭绝。这意味着随机扰动有利于流行病的控制。为了说明性能的理论结果，我们提出了一系列的数值模拟这些情况下，相对于不同的噪声干扰系数。(C)2015 Elsevier Inc. All rights reserved.
In this paper, we propose new mathematical models with nonlinear incidence rate and double epidemic hypothesis. Then we dedicate to develop a method to obtain the threshold of the stochastic SIS epidemic model. To this end, first, we investigate the stability of the equilibria of the deterministic system and obtain the conditions for the extinction and the permanence of two epidemic diseases. Second, we explore and obtain the threshold of a stochastic SIS system for the extinction and the permanence in mean of two epidemic diseases. The results show that a large stochastic disturbance can cause infectious diseases to go to extinction, in other words, the persistent infectious disease of a deterministic system can become extinct due to the white noise stochastic disturbance. This implies that the stochastic disturbance is conducive to epidemic diseases control. To illustrate the performance of the theoretical results, we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients. (C) 2015 Elsevier Inc. All rights reserved.