We propose a mathematical model to understand the transmission dynamics of HIV/AIDS in an environment. In addition to previous approaches, we incorporate two classes of isolated. By isolated we do not mean physical separation, but commitment to keep its status. We establish the well-posedness of our model and fully analyze the asymptotic behavior of the solutions which depends on the basic reproduction number $$R_{0}$$ . We then perform sensitive analysis to investigate the best strategy to keep the average number of secondary infection $$R_{0}$$ low. Our investigation reveals that when there is both high awareness and high efficacy of PrEP (pre-exposure prophylaxis) use, increasing the efficacy of PrEP use decreases $$R_{0}$$ the most. Otherwise, the best strategy is to isolated more susceptible to the class $$H_{1}$$ . Our model can be applied to any organizations/companies relying on physical labor forces (with some workers being infected by HIV/AIDS).

中文翻译：

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非经典隔离的暴露前预防 HIV/AIDS 数学模型

我们提出了一个数学模型来了解环境中 HIV/AIDS 的传播动态。除了以前的方法之外，我们还合并了两类隔离。我们所说的孤立并不是指身体上的分离，而是承诺保持其地位。我们建立了模型的适定性，并充分分析了依赖于基本再生数 $$R_{0}$$ 的解决方案的渐近行为。然后，我们执行敏感分析以研究将继发感染的平均数量 $$R_{0}$$ 保持在较低水平的最佳策略。我们的调查显示，当对 PrEP（暴露前预防）使用的认知度和功效都很高时，提高 PrEP 使用的功效会最大程度地降低 $$R_{0}$$。否则，最好的策略是隔离更容易受到类 $$H_{1}$$ 的影响。