Near-Optimal Spectral Disease Mitigation in Healthcare Facilities

Healthcare associated infections (HAIs) impose a substantial burden, both on patients and on the healthcare system. Designing effective strategies by using interventions such as vaccination, isolation, cleaning, mobility modification, etc., to reduce HAI spread is an important computational challenge. Spectral approaches are quite useful for modeling and solving problems of reducing disease spread over contact networks, but they have not been used for disease-spread models and contact networks that are specific for HAIs. Our main contribution in this paper is to close this gap. We make 3 specific contributions. (i) We present the first epidemic threshold results on temporal bipartite networks, i.e., a time-varying sequence of bipartite people-location network, for the Susceptible-Infected-Susceptible (SIS) model. (ii) We leverage our epidemic threshold result to pose the HAI mitigation problem as minimizing the spectral radius of the system matrix, while removing few nodes or edges. We present a scalable combinatorial algorithm that provides approximation guarantees. (iii) Through extensive experiments on actual healthcare contact networks derived from operations data from the University of Iowa Hospitals and Clinics, Carilion Clinic, and several other healthcare facilities, we show that our algorithm consistently outperforms a number of baselines (random, degree, top-k, eigen centrality) both in terms of reducing the spectral radius of the system matrix and in terms of reducing infections.