Excellence in Research: Mathematical Analysis of the Prevention of HIV with PrEP and HAART Treatment

几十年来，预防、减轻和根除艾滋病毒一直是各国政府、科学家和公共卫生专业人员关注的焦点。最近的报告，如美国卫生与公众服务部分发的《终结艾滋病毒流行：美国计划》，为全世界数百万受这一疾病影响的人带来了新的希望。为了实现这一目标，必须了解如何最有效地利用现有资源，考虑到新的预防治疗和高度有效的抗逆转录病毒治疗的不断改进，特别是在不遵守规定的情况下。一个现实的数学模型，包括这两种处理，以及对不同亚群的不成比例的影响，是有效利用资源的必要条件。从公共卫生的角度来看，这一提议的广泛影响是深远的，但也将作为一个平台，在数学和医学的界面上培养主要代表性不足的本科生和研究生。霍华德大学、马里兰大学、巴尔的摩县和美国国立卫生研究院的研究人员之间的合作将培养学生在协作团队环境中工作，专注于解决一个紧迫的科学问题。现实的数学模型可以提出可以显著减少艾滋病毒感染人数的最佳干预方案。暴露前预防治疗（PrEP）的效果将包括在先前开发的艾滋病毒数学模型中。以前的不完善疫苗模型显示，可能出现向后分叉，从而极大地影响流行病的动态。因此，使没有疫苗的模型达到无病平衡的干预措施，也可以使有PrEP的模型达到稳定的地方性平衡。艾滋病毒的传播取决于受感染个体的病毒载量。因此，现实的数学模型必须包括非稳定的高活性抗逆转录病毒治疗（HAART）的影响，包括有组织的治疗中断、缺乏对药物治疗方案的坚持和耐药性。非稳定的HAART治疗方案以及随后在病毒抑制和慢性感染之间的双向运动将需要在模型中使用非指数治疗阶段，该模型将适用于约翰霍普金斯大学彭博公共卫生学院公开提供的多中心艾滋病队列研究（MACS）数据。由于数学模型将使用公共卫生数据，因此将从结构上和实践上解决参数可识别性问题。将使用几个数值工具来获取模型的结构可识别性。轮廓似然方法将用于评估模型参数的实际可识别性，并为参数估计提供置信区间。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Prevention, mitigation, and eradication of HIV has been the focus of governments, scientists, and public health professionals for decades. Recent reports, such as the “Ending the HIV Epidemic: A Plan for America” distributed by the US Department of Health and Human Services, have generated a renewed hope for the millions of people around the world affected by this disease. To achieve this goal, it is imperative to understand the most effective use of available resources in light of the new prophylaxis treatment and the continued improvements of the highly active anti-retroviral treatment, particularly in the case of non-compliance. A realistic mathematical model, including these two treatments, as well as disproportional effects on disparate subpopulations, is essential for effective resource utilization. The broader impacts of this proposal are far-reaching from a public health perspective, but will also serve as a platform to train primarily underrepresented undergraduate and graduate students at the interface of mathematics and medicine. This collaboration between researchers at Howard University, University of Maryland, Baltimore County, and the National Institutes of Health will train students to work in a collaborative team environment focused on addressing a pressing scientific problem.Realistic mathematical models can suggest best courses of intervention that can significantly reduce the number of HIV infections. The effect of the pre-exposure prophylaxis treatment (PrEP) will be included in a previously developed mathematical model of HIV. Previous models of imperfect vaccines have shown the potential for a backwards bifurcation that can dramatically affect the dynamics of the epidemic. As a result, the same intervention that brings a model without a vaccine to the disease-free equilibrium, could drive the dynamics of the model with PrEP to a stable endemic equilibrium. Transmission of HIV depends on the viral-load of the infected individual. Thus, realistic mathematical models must include the effect of non-steady highly active anti-retroviral treatment (HAART) through structured treatment interruptions, lack of adherence to drug regimen and drug resistance. Non-steady HAART treatment regimes and the subsequent two-way movement between virally suppressed and chronically infected will require using non-exponential treatment stages into the model, which will be fitted to publicly available Multicenter AIDS Cohort Study (MACS) data from the Johns Hopkins Bloomberg School of Public Health. Since public health data will be used in the mathematical model, parameter identifiability will be addressed structurally and practically. Several numerical tools for accessing structural identifiability of the model will be used. The profile likelihood method will be used to assess the practical identifiability of model parameters and to provide confidence intervals for parameter estimation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.