Article (2024)
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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.
Uncontrolled Keywords
SIR model; jump-diffusion processes; parameter estimation; dynamic programming; homing problem
| Subjects: |
2950 Applied mathematics > 2957 Mathematical biology and physiology 2950 Applied mathematics > 2960 Mathematical modelling |
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| Department: | Department of Mathematics and Industrial Engineering |
| Funders: | NSERC / CRSNG |
| PolyPublie URL: | https://publications.polymtl.ca/58791/ |
| Journal Title: | Mathematics (vol. 12, no. 13) |
| Publisher: | MDPI |
| DOI: | 10.3390/math12132139 |
| Official URL: | https://doi.org/10.3390/math12132139 |
| Date Deposited: | 30 Jul 2024 16:10 |
| Last Modified: | 07 Aug 2024 15:42 |
| Cite in APA 7: | Lefebvre, M. (2024). Modeling and optimal control of infectious diseases. Mathematics, 12(13), 2139 (12 pages). https://doi.org/10.3390/math12132139 |
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