Network-Based Interventions for HIV Prevention via Cascade-Aware Suppression of Transmission

TL;DR

This paper introduces CAST, a novel approximation algorithm for optimizing resource distribution in HIV transmission networks to minimize new infections, demonstrating superior performance over existing methods.

Contribution

The work formalizes a new constrained optimization problem for HIV intervention and proposes CAST, a polynomial-time approximation algorithm with proven theoretical guarantees.

Findings

CAST outperforms standard baselines in real-world HIV network evaluations.

CAST is robust across diverse infectious disease networks and data imperfections.

The problem is connected to the Minimum-$k$-Union problem and concentration bounds.

Abstract

Treating and preventing Human Immunodeficiency Virus (HIV) remains a critical global health challenge. While antiretroviral therapy provides a path toward viral suppression -- effectively eliminating an individual's transmission risk -- systemic resource constraints limit the reach of intervention efforts. This work addresses the strategic distribution of intensive resources among virally unsuppressed individuals to minimize the expected cascade of new infections within a transmission network. We formalize this challenge as a novel constrained optimization problem where we have resources to "treat" $k$ out of a set $\mathbf{P}$ of virally unsuppressed individuals, and establish its theoretical connections to existing computational literature. We then propose Cascade-Aware Suppression of Transmission (CAST), a polynomial-time $(\delta, \epsilon)$-approximation algorithm that achieves a $2\sqrt{|\mathbf{P}|}$ approximation ratio by leveraging connections to the Minimum-$k$-Union (MkU) problem and Hoeffding-style concentration bounds. Extensive evaluations on real-world HIV networks demonstrate that CAST outperforms standard public health and computer science baselines. Furthermore, we show that CAST is empirically robust across diverse infectious disease networks, varied edge probability initializations, and settings involving imperfect network data.