Stochastic optimal control of pre-exposure prophylaxis for HIV infection for a jump model.
HIV
Pre-exposure prophylaxis
Simulations
Stochastic control
Stochastic differential equations with jumps
Journal
Journal of mathematical biology
ISSN: 1432-1416
Titre abrégé: J Math Biol
Pays: Germany
ID NLM: 7502105
Informations de publication
Date de publication:
29 Oct 2024
29 Oct 2024
Historique:
received:
27
02
2024
accepted:
02
10
2024
revised:
06
09
2024
medline:
29
10
2024
pubmed:
29
10
2024
entrez:
29
10
2024
Statut:
epublish
Résumé
We analyze a stochastic optimal control problem for the PReP vaccine in a model for the spread of HIV. To do so, we use a stochastic model for HIV/AIDS with PReP, where we include jumps in the model. This generalizes previous works in the field. First, we prove that there exists a positive, unique, global solution to the system of stochastic differential equations which makes up the model. Further, we introduce a stochastic control problem for dynamically choosing an optimal percentage of the population to receive PReP. By using the stochastic maximum principle, we derive an explicit expression for the stochastic optimal control. Furthermore, via a generalized Lagrange multiplier method in combination with the stochastic maximum principle, we study two types of budget constraints. We illustrate the results by numerical examples, both in the fixed control case and in the stochastic control case.
Identifiants
pubmed: 39470810
doi: 10.1007/s00285-024-02151-3
pii: 10.1007/s00285-024-02151-3
doi:
Substances chimiques
Anti-HIV Agents
0
AIDS Vaccines
0
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
55Subventions
Organisme : Ministarstvo Prosvete, Nauke i Tehnološkog Razvoja
ID : 451-03-65/2024-03/200124
Informations de copyright
© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
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