标题： 优先级PrEP在HIV预防中的溢出效应的分析和数值方法 显示英文标题

标题： Analytical and numerical methods for spillover effects in prioritized PrEP for HIV prevention

摘要： 暴露前预防（PrEP）是一种有效防止HIV传播的干预措施，但其高成本和不均衡的使用率带来了挑战。 虽然溢出效应——即某一群体使用PrEP会减少其他群体的感染——已被知晓，但它们仍难以量化，很少指导政策。 我们开发并分析了一个新颖的分 compartment HIV 模型，将人群分为三个相互作用的子群：异性恋男性（HETM）、异性恋女性（HETF）和与男性发生性关系的男性（MSM）。 我们推导了标准结果，包括控制繁殖数，并建立了疾病自由平衡点的局部和全局稳定性的条件。 我们提供了溢出调整后的需要治疗人数（NNT）的显式、时间解析表达式，这是一种衡量一个群体中PrEP使用对其他群体发病率影响的指标。 校准到佐治亚州省级数据的模拟显示，向MSM提供PrEP产生了显著的间接效益，特别是对于HETF，其溢出效应是直接效应的五倍。 我们将基准模型扩展为包括HETF内的风险分层，表明针对高风险的HETF优于直接向HETM提供PrEP，强调了组内异质性的重要性。 为了评估这些发现是否在更详细的假设下仍然成立，我们将我们的框架嵌入到由CDC维护的全国HOPE模型中，并使用Sobol指数进行全局敏感性分析。 这种方法扩展了我们的分析见解，并量化了PrEP分配策略中的不确定性如何通过复杂动态传播。 我们的结果表明，适度复杂的、可分析的模型可以为HIV控制提供现实且可行的指导——在保持可解释性的同时，捕捉非线性溢出动态，即使在高维设置中也是如此。 显示英文摘要

摘要： Pre-exposure prophylaxis (PrEP) is a highly effective intervention for preventing HIV transmission, but its high cost and uneven uptake raise challenges. While spillover effects - wherein PrEP use in one group reduces infections in others - are known to occur, they remain poorly quantified and rarely guide policy. We develop and analyze a novel compartmental HIV model that stratifies the population into three interacting subgroups: heterosexual males (HETM), heterosexual females (HETF), and men who have sex with men (MSM). We derive standard results, including the control reproduction number, and establish conditions for local and global stability of the disease-free equilibrium. We provide a closed-form, time-resolved expression for the spillover-adjusted number needed to treat (NNT), a measure of the population-level impact of PrEP uptake in one group on incidence in others. Simulations calibrated to Georgia state-level data reveal that PrEP delivery to MSM yields substantial indirect benefits, particularly for HETF, where the spillover effect exceeds the direct effect by a factor of five. We extend the baseline model to include risk stratification within HETF, showing that targeting high-risk HETF outperforms direct PrEP delivery to HETM, emphasizing the importance of intra-group heterogeneity. To evaluate whether these findings persist under more detailed assumptions, we embed our framework into the national HOPE model maintained by the CDC and conduct global sensitivity analysis using Sobol indices. This approach extends our analytical insights and quantifies how uncertainty in PrEP allocation strategies propagates through complex dynamics. Our results show that moderately complex, analytically tractable models can yield realistic and actionable guidance for HIV control-capturing nonlinear spillover dynamics in ways that remain interpretable even in high-dimensional settings.