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

TL;DR

The results show that spillover is a central driver of PrEP dynamics and that failing to account for it risks mis-allocating resources.

Abstract

Pre-exposure prophylaxis (PrEP) is an effective intervention for preventing HIV transmission, but high cost and uneven uptake raise challenges for resource allocation. 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 provide a comprehensive modeling study for PrEP spillover across risk groups, and develop analytic and numerical tools for its quantification. We first develop a compartmental model for HIV transmission that stratifies the population into interacting subgroups: heterosexual males (HETM), high- and low-risk heterosexual females (HETF-hi/HETF-lo) and men who have sex with men (MSM). The asymptotic stability of the disease-free equilibrium of the model is analyzed. Spillover is quantified by deriving an expression for the spillover-adjusted number needed to treat (NNT), a measure of the population-level impact of PrEP. Simulations show PrEP delivery to MSM yields substantial indirect benefits, particularly for HETF-lo, where spillover exceeds the direct effect by a factor of five. We show targeting HETF-hi outperforms direct PrEP delivery to HETM, emphasizing the importance of intra-group heterogeneity. To evaluate whether these results hold under more detailed assumptions, we embed our framework into the national HOPE model maintained by the Centers for Disease Control and Prevention (CDC) and conduct global sensitivity analysis using Sobol indices with Polynomial Chaos Expansion. This approach extends our analytical insights and quantifies how uncertainty in PrEP allocation propagates through complex dynamics. Further, this framework provides a numerical procedure for quantifying spillover where direct analysis is impractical. Our results show that spillover is a central driver of PrEP dynamics and that failing to account for it risks mis-allocating resources.

Figures (5)

• Figure 1: Contact structure of the model \ref{['basicmodel']}.
• Figure 2: Model calibration and prediction for the total and cumulative HIV cases for the U.S. state of Georgia using HIV surveillance data for the period 2017-2019 ATLAS (model predictions given for the period from 2020 to 2030). Left (right) panel: total (cumulative) number of people living with HIV in each of the four risk groups in Georgia, as a function of time. Parameter and initial values used in the model calibration and prediction are as given by the baseline values in Table \ref{['tab:riskStructuredModelParameters']}.
• Figure 3: Assessment of PrEP spillover on HIV incidence in the US state of Georgia for the period from 2017 to 2030. Simulations of the model \ref{['basicmodel']} showing new cases averted per person on PrEP, as a function of time. Effect of PrEP usage on HIV incidence in MSM (top-left panel), high-risk HETF (top-right panel), low-risk HETF (bottom-left panel) and HETM (bottom-right panel) populations. Parameter and initial values used in the simulations are as given in Table \ref{['tab:riskStructuredModelParameters']}.
• Figure 4: Simulations of the model \ref{['basicmodel']} showing number needed to treat (i.e., number needed to be on PrEP) to save one new HIV case in the respective risk group, as a function of time. MSM (top-left panel), high-risk HETF (top-right panel), low-risk HETF (bottom-left panel), and HETM (bottom-right panel). Parameter and initial values used in the simulation are as given in Table \ref{['tab:riskStructuredModelParameters']}.
• Figure 5: HOPE model, simulation study: Total Sobol indices.

Theorems & Definitions (13)

• Theorem 2.1
• proof
• Theorem 2.2
• Proposition 2.3
• proof
• Remark 2.4
• Remark 3.1
• Remark 3.2
• Theorem \ref{las_basicmodel}
• Theorem \ref{las_basicmodel}