Modeling and Designing Non-Pharmaceutical Interventions in Epidemics: A Submodular Approach
Shiyu Cheng, Luyao Niu, Bhaskar Ramasubramanian, Andrew Clark, Radha Poovendran
TL;DR
The paper tackles designing cost-effective non-pharmaceutical interventions (NPIs) to slow an epidemic on a networked SIS model by leveraging a mean-field, quasi-stationary endemic distribution with ${\mathcal{R}_0 = \rho(D^{-1}BA)}$ as the outbreak threshold. It introduces cluster-based NPIs that reduce edge weights to ${a_{ij}(\overline{S})}$ and proves that the end-state constraint can be relaxed into a submodular, greedy-optimizable form, yielding a submodular-cost submodular-cover (SCSC) problem with provable guarantees. The authors provide a detailed formulation of the cost components ${\mathcal{C}_1,\mathcal{C}_2,\mathcal{C}_3}$ and demonstrate the submodular structure, enabling scalable solution via greedy surrogates. Through simulations on Watts-Strogatz networks, the method achieves substantial infection reduction relative to baselines while reducing NPI costs, illustrating practical applicability for public-health decision-making. The work thus offers a principled, scalable framework for cluster-based NPIs that balances epidemiological impact and economic considerations.
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.