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Dynamical analysis of a stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis

机译：带有非线性传染率和双重流行病假设的随机SIS传染病模型的动力学分析

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摘要

In this paper, a stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis is proposed and analysed. We explain the effects of stochastic disturbance on disease transmission. To this end, firstly, we investigated the dynamic properties of the system neglecting stochastic disturbance and obtained the threshold and the conditions for the extinction and the permanence of two kinds of epidemic diseases by considering the stability of the equilibria of the deterministic system. Secondly, we paid prime attention on the threshold dynamics of the stochastic system and established the conditions for the extinction and the permanence of two kinds of epidemic diseases. We found that there exists a significant difference between the threshold of the deterministic system and that of the stochastic system. Moreover, it has been established that the persistent of infectious disease analysed by use of deterministic system becomes extinct under the same conditions due to the stochastic disturbance. This implies that a stochastic disturbance has significant impact on the spread of infectious diseases and the larger stochastic disturbance leads to control the epidemic diseases. In order to illustrate the dynamic difference between the deterministic system and the stochastic system, there have been given a series of numerical simulations by using different noise disturbance coefficients.
机译：提出并分析了具有非线性发生率和双重流行病假说的随机SIS流行病模型。我们解释了随机干扰对疾病传播的影响。为此，首先，我们考虑了确定性系统均衡的稳定性，研究了忽略随机扰动的系统的动力学特性，并确定了两种流行病的灭绝和持久性的阈值和条件。其次，我们高度关注随机系统的阈值动态，并为两种流行病的灭绝和持续性建立了条件。我们发现，确定性系统的阈值与随机系统的阈值之间存在显着差异。而且，已经确定的是，在相同条件下，由于随机干扰，使用确定性系统分析的传染病持续性已消失。这意味着，随机干扰对传染病的传播具有重大影响，而较大的随机干扰导致控制流行病。为了说明确定性系统和随机性系统之间的动态差异，通过使用不同的噪声干扰系数进行了一系列数值模拟。

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