Modeling and Designing Non-Pharmaceutical Interventions in Epidemics: A Submodular Approach

TL;DR

This paper develops a polynomial-time method for designing cost-effective non-pharmaceutical interventions to control epidemic spread, using a submodular optimization approach based on steady-state epidemic modeling.

Contribution

It introduces a novel submodular optimization framework for NPI strategy design under a steady-state epidemic model, enabling efficient and effective intervention planning.

Findings

NPI strategies can reduce infection probabilities below target thresholds.

The submodular approach allows polynomial-time optimization for epidemic control.

Experimental results demonstrate the effectiveness of the proposed method on network models.

Abstract

This paper considers the problem of designing non-pharmaceutical intervention (NPI) strategies, such as masking and social distancing, to slow the spread of a viral epidemic. We formulate the problem of jointly minimizing the infection probabilities of a population and the cost of NPIs based on a Susceptible-Infected-Susceptible (SIS) propagation model. To mitigate the complexity of the problem, we consider a steady-state approximation based on the quasi-stationary (endemic) distribution of the epidemic, and prove that the problem of selecting a minimum-cost strategy to satisfy a given bound on the quasi-stationary infection probabilities can be cast as a submodular optimization problem, which can be solved in polynomial time using the greedy algorithm. We carry out experiments to examine effects of implementing our NPI strategy on propagation and control of epidemics on a Watts-Strogatz small-world graph network. We find the NPI strategy reduces the steady state of infection probabilities of members of the population below a desired threshold value.