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Modeling and Optimal Control of Infectious Diseases

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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)

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.

Suggested Citation

  • Mario Lefebvre, 2024. "Modeling and Optimal Control of Infectious Diseases," Mathematics, MDPI, vol. 12(13), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2139-:d:1430589
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    References listed on IDEAS

    as
    1. Zhou, Yanli & Zhang, Weiguo, 2016. "Threshold of a stochastic SIR epidemic model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 204-216.
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