在这篇文章中,我们提出了人类免疫缺陷病毒(HIV)/获得性免疫缺陷综合征(AIDS)的数学模型,考虑到CD4+T细胞的数量和抗逆转录病毒治疗。该模型是基于易感因素开发的,感染,治疗,艾滋病(SITA)框架,其中基于CD4+T细胞的数量划分感染的和处理的区室。此外,我们考虑治疗失败的可能性,这可能会加剧受治疗个体的状况。最初,我们分析了一个简化的HIV/AIDS模型,没有区分感染和治疗类别。我们的发现表明,无HIV/AIDS平衡点的全球稳定性取决于基本繁殖数小于1。此外,分叉分析表明,我们的简化模型在复制数等于1时始终表现出跨临界分叉。在完整的模型中,我们阐明对照复制数如何决定无HIV/AIDS平衡点的稳定性.为了使我们的模型与经验数据保持一致,我们使用来自受艾滋病毒/艾滋病影响最大的四个国家的患病率数据来估计其参数,即,埃斯瓦蒂尼,莱索托,博茨瓦纳,和南非。我们采用数值模拟并进行弹性和灵敏度分析,以检查我们的模型参数如何影响控制再现数和每个模型隔室的动力学。我们的研究结果表明,每个国家对模型参数表现出不同的敏感性,这意味着需要根据目标国家制定量身定制的战略。自主模拟强调了病例检测和使用避孕套在降低艾滋病毒/艾滋病流行方面的潜力。此外,我们发现避孕套的质量起着至关重要的作用:有了更高质量的避孕套,较小比例的感染者需要使用它们来从人群中根除艾滋病毒/艾滋病。在我们的最优控制模拟中,当控制干预被视为时间相关变量时,我们评估人群行为。我们的分析表明,避孕套的使用和病例检测相结合,作为随时间变化的变量,可以显着减少艾滋病毒的传播,同时保持最佳的干预成本。此外,我们的成本效益分析表明,单独使用避孕套干预就成为最具成本效益的策略,然后是病例检测和避孕套使用的组合,最后,案例检测作为一种独立的策略。
In this article, we present a mathematical model for human immunodeficiency virus (HIV)/Acquired immune deficiency syndrome (AIDS), taking into account the number of CD4+T cells and antiretroviral treatment. This model is developed based on the susceptible, infected, treated, AIDS (SITA) framework, wherein the infected and treated compartments are divided based on the number of CD4+T cells. Additionally, we consider the possibility of treatment failure, which can exacerbate the condition of the treated individual. Initially, we analyze a simplified HIV/AIDS model without differentiation between the infected and treated classes. Our findings reveal that the global stability of the HIV/AIDS-free equilibrium point is contingent upon the basic reproduction number being less than one. Furthermore, a bifurcation analysis demonstrates that our simplified model consistently exhibits a transcritical bifurcation at a reproduction number equal to one. In the complete model, we elucidate how the control reproduction number determines the stability of the HIV/AIDS-free equilibrium point. To align our model with the empirical data, we estimate its parameters using prevalence data from the top four countries affected by HIV/AIDS, namely, Eswatini, Lesotho, Botswana, and South Africa. We employ numerical simulations and conduct elasticity and sensitivity analyses to examine how our model parameters influence the control reproduction number and the dynamics of each model compartment. Our findings reveal that each country displays distinct sensitivities to the model parameters, implying the need for tailored strategies depending on the target country. Autonomous simulations highlight the potential of case detection and
condom use in reducing HIV/AIDS prevalence. Furthermore, we identify that the quality of condoms plays a crucial role: with higher quality condoms, a smaller proportion of infected individuals need to use them for the potential eradication of HIV/AIDS from the population. In our optimal control simulations, we assess population behavior when control interventions are treated as time-dependent variables. Our analysis demonstrates that a combination of
condom use and case detection, as time-dependent variables, can significantly curtail the spread of HIV while maintaining an optimal cost of intervention. Moreover, our cost-effectiveness analysis indicates that the
condom use intervention alone emerges as the most cost-effective strategy, followed by a combination of case detection and
condom use, and finally, case detection as a standalone strategy.