Limiting Disease Spreading in Human Networks
Gargi Bakshi, Sujoy Bhore, Suraj Shetiya
TL;DR
This work addresses limiting disease spread in spatial human networks by applying diffusion models (linear threshold and independent cascade) on generalized Waxman random geometric graphs. It establishes that the containment objective is not submodular or supermodular, and thus lacks guaranteed greedy approximations, motivating a practical algorithmic suite: sampling topologies, a binary linear program with relaxations, two rounding schemes (top-k and iterative), plus greedy and local-search methods, with iterative rounding for efficiency. The authors provide thorough runtime analyses and compare approaches against exact ILP on manageable instances, showing LP-based rounding (especially LP-TKR) delivers near-optimal solutions with substantial speed-ups. Experiments on Gaussian Waxman, Erdős–Rényi graphs, and real Texas/New York datasets under LT and IC demonstrate strong performance of the LP-rounding methods, alongside competitive greedy and local-search baselines, highlighting practical applicability for resource-constrained vaccination strategies in spatially structured populations. The work lays a foundation for scalable, data-driven vaccine allocation in realistic networks and motivates further theoretical investigation into approximation guarantees and alternative diffusion models.
Abstract
The outbreak of a pandemic, such as COVID-19, causes major health crises worldwide. Typical measures to contain the rapid spread usually include effective vaccination and strict interventions (Nature Human Behaviour, 2021). Motivated by such circumstances, we study the problem of limiting the spread of a disease over a social network system. In their seminal work (KDD 2003), Kempe, Kleinberg, and Tardos introduced two fundamental diffusion models, the linear threshold and independent cascade, for the influence maximization problem. In this work, we adopt these models in the context of disease spreading and study effective vaccination mechanisms. Our broad goal is to limit the spread of a disease in human networks using only a limited number of vaccines. However, unlike the influence maximization problem, which typically does not require spatial awareness, disease spreading occurs in spatially structured population networks. Thus, standard Erdos-Renyi graphs do not adequately capture such networks. To address this, we study networks modeled as generalized random geometric graphs, introduced in the seminal work of Waxman (IEEE J. Sel. Areas Commun. 1988). We show that for disease spreading, the optimization function is neither submodular nor supermodular, in contrast to influence maximization, where the function is submodular. Despite this intractability, we develop novel algorithms leveraging local search and greedy techniques, which perform exceptionally well in practice. We compare them against an exact ILP-based approach to further demonstrate their robustness. Moreover, we introduce an iterative rounding mechanism for the relaxed LP formulation. Overall, our methods establish tight trade-offs between efficiency and approximation loss.