Abstract The world of uncertainty motivates the study of stochastic perturbation in the mathematical models of real life. The main objective of this paper is to study stochastic sex-structured HIV/AIDS epidemic model with effect of screening of infectives. We have shown that the proposed stochastic epidemic model with boundedness and permanence has a unique global positive solution. The selection of suitable Lyapunov functions provides sufficient conditions for investigating persistence and extinction of disease. Based on numerical experiments, the theoretical findings of this paper have been verified.

中文翻译：

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具有感染者筛查效应的随机性别结构HIV/AIDS流行模型的精确解分析

摘要 不确定性世界激发了对现实生活数学模型中随机扰动的研究。本文的主要目的是研究具有感染者筛查效应的随机性别结构的HIV/AIDS流行模型。我们已经证明，所提出的具有有界性和永久性的随机流行病模型具有独特的全局正解。选择合适的李雅普诺夫函数为研究疾病的持久性和灭绝性提供了充分的条件。通过数值实验验证了本文的理论结论。