The purpose of this paper is to investigate the stability of a deterministic and stochastic SIS epidemic model with double epidemic hypothesis and specific nonlinear incidence rate. We prove the local asymptotic stability of the equilibria of the deterministic model. Moreover, by constructing a suitable Lyapunov function, we obtain a sufficient condition for the global stability of the disease-free equilibrium. For the stochastic model, we establish global existence and positivity of the solution. Thereafter, stochastic stability of the disease-free equilibrium in almost sure exponential and th moment exponential is investigated. Finally, numerical examples are presented.

中文翻译：

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具有双重流行病假设和特定功能响应的确定性和随机SIS流行病模型的分析

本文的目的是研究具有双重流行病假设和特定非线性发生率的确定性和随机SIS流行病模型的稳定性。我们证明了确定性模型均衡的局部渐近稳定性。此外，通过构建合适的Lyapunov函数，我们为无病平衡的全局稳定性提供了充分的条件。对于随机模型，我们建立了解的整体存在性和正性。此后，研究了几乎确定的指数和th矩指数下无病平衡的随机稳定性。最后，给出了数值示例。