Modeling and Optimal Control of Infectious Diseases

Mario Lefebvre ()
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Mario Lefebvre: Department of Mathematics and Industrial Engineering, Polytechnique Montréal, C.P. 6079, Succursale Centre-ville, Montréal, QC H3C 3A7, Canada

Mathematics, 2024, vol. 12, issue 13, 1-12

Abstract: We propose a stochastic model of infectious disease transmission that is more realistic than those found in the literature. The model is based on jump-diffusion processes. However, it is defined in such a way that the number of people susceptible to be infected decreases over time, which is the case for a population of fixed size. Next, we consider the problem of finding the optimal control of the proposed model. The dynamic programming equation satisfied by the value function is derived. Estimators of the various model parameters are obtained.

Keywords: SIR model; jump-diffusion processes; parameter estimation; dynamic programming; homing problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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