Epidemic control via stochastic optimal control

2020/04/14 by Andrew Lesniewski, Lesniewski, Andrew
Economics, Econometrics and Finance · Mathematics · #COVID-19 epidemiological studies #Computational Finance (q-fin.CP) #Econometrics (econ.EM) #FOS: Biological sciences #FOS: Economics and business #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Populations and Evolution (q-bio.PE) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2004.06680

openalex publication_date 2020/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the problem of optimal control of the stochastic SIR model. Models of this type are used in mathematical epidemiology to capture the time evolution of highly infectious diseases such as COVID-19. Our approach relies on reformulating the Hamilton-Jacobi-Bellman equation as a stochastic minimum principle. This results in a system of forward backward stochastic differential equations, which is amenable to numerical solution via Monte Carlo simulations. We present a number of numerical solutions of the system under a variety of scenarios.

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