Controlling the Spread of Epidemics on Networks with Differential Privacy

TL;DR

This paper develops differentially private algorithms for epidemic control on networks, enabling effective vaccination strategies while preserving contact data privacy, and demonstrates their practical utility on various networks.

Contribution

Introduces $( ext{} ext{ extepsilon}, ext{ extdelta})$-differentially private algorithms for vaccination strategies based on network property control, using a novel private multi-set multi-cover approach.

Findings

Algorithms effectively reduce maximum degree and spectral radius under privacy constraints.

Demonstrates privacy-utility tradeoffs on synthetic and real-world networks.

Strategies maintain effectiveness while ensuring data privacy.

Abstract

Designing effective strategies for controlling epidemic spread by vaccination is an important question in epidemiology, especially in the early stages when vaccines are limited. This is a challenging question when the contact network is very heterogeneous, and strategies based on controlling network properties, such as the degree and spectral radius, have been shown to be effective. Implementation of such strategies requires detailed information on the contact structure, which might be sensitive in many applications. Our focus here is on choosing effective vaccination strategies when the edges are sensitive and differential privacy guarantees are needed. Our main contributions are $(\varepsilon,\delta)$-differentially private algorithms for designing vaccination strategies by reducing the maximum degree and spectral radius. Our key technique is a private algorithm for the multi-set multi-cover problem, which we use for controlling network properties. We evaluate privacy-utility tradeoffs of our algorithms on multiple synthetic and real-world networks, and show their effectiveness.