Abstract

In this paper, we propose and study a higher order stochastically perturbed SICA epidemic model for HIV transmission. We obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a series of suitable Lyapunov functions. In a biological point of view, the existence of a stationary distribution indicates that the infectious disease will be prevalent and persistent in the population. Moreover, we make up adequate conditions for complete eradication and wiping out of the infectious disease.

中文翻译：

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具有高阶扰动的HIV传播随机SICA流行病模型的动力学

摘要

在本文中，我们提出并研究了一种用于HIV传播的高阶随机扰动SICA流行病模型。通过建立一系列合适的Lyapunov函数，我们为系统正解的遍历平稳分布的存在和唯一性提供了充分的条件。从生物学的角度来看，固定分布的存在表明传染病将在人群中普遍存在并持续存在。此外，我们为彻底根除和消除传染病创造了充分的条件。