Business Publications
Document Type
Article
Publication Date
12-2019
Volume
67
Issue
3
Journal
Operations Research
URL with Digital Object Identifier
https://doi.org/10.1287/opre.2018.1817
Abstract
Antimicrobial resistance is a significant public health threat. In the U.S. alone, 2 million people are infected and 23,000 die each year from antibiotic resistant bacterial infections. In many cases, infections are resistant to all but a few remaining drugs. We examine the case where a single drug remains and solve for optimal treatment policy for an SIS infectious disease model incorporating the effects of drug resistance. The problem is formulated as an optimal control problem with two continuous state variables, the disease prevalence and drug's "quality" (the fraction of infections that are drug-susceptible). The decision maker's objective is to minimize the discounted cost of the disease to society over an infinite horizon. We provide a new generalizable solution approach that allows us to thoroughly characterize the optimal treatment policy analytically. We prove that the optimal treatment policy is a bang-bang policy with a single switching time. The action/inaction regions can be described by a single boundary that is strictly increasing when viewed as a function of drug quality, indicating that, when the disease transmission rate is constant, the policy of withholding treatment to preserve the drug for a potentially more serious future outbreak is not optimal. We show that the optimal value function and/or its derivatives are neither C1 nor Lipschitz continuous suggesting that numerical approaches to this family of dynamic infectious disease models may not be computationally stable. Furthermore, we demonstrate that relaxing the standard assumption of constant disease transmission rate can fundamentally change the shape of the action region, add a singular arc to the optimal control, and make preserving the drug for a serious outbreak optimal. In addition, we apply our framework to the case of antibiotic resistant gonorrhea.
Notes
This is the authors' version of the article published in Operations Research and available at https://doi.org/10.1287/opre.2018.1817