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Article

Modeling and Optimal Control of Infectious Diseases

Department of Mathematics and Industrial Engineering, Polytechnique Montréal, C.P. 6079, Succursale Centre-ville, Montréal, QC H3C 3A7, Canada
Mathematics 2024, 12(13), 2139; https://doi.org/10.3390/math12132139
Submission received: 3 June 2024 / Revised: 23 June 2024 / Accepted: 30 June 2024 / Published: 7 July 2024

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 SIR model; jump-diffusion processes; parameter estimation; dynamic programming; homing problem

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MDPI and ACS Style

Lefebvre, M. Modeling and Optimal Control of Infectious Diseases. Mathematics 2024, 12, 2139. https://doi.org/10.3390/math12132139

AMA Style

Lefebvre M. Modeling and Optimal Control of Infectious Diseases. Mathematics. 2024; 12(13):2139. https://doi.org/10.3390/math12132139

Chicago/Turabian Style

Lefebvre, Mario. 2024. "Modeling and Optimal Control of Infectious Diseases" Mathematics 12, no. 13: 2139. https://doi.org/10.3390/math12132139

APA Style

Lefebvre, M. (2024). Modeling and Optimal Control of Infectious Diseases. Mathematics, 12(13), 2139. https://doi.org/10.3390/math12132139

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