Non-Pharmaceutical Interventions and Vaccination Controls in a Stochastic SIVR Epidemic Model

In this paper, we study an optimal control problem for a generalized stochastic SIVR model as well as for the corresponding deterministic model. We consider two control strategies in the optimal control model, namely: the successful practice of non-pharmaceutical interventions and vaccination for su...

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Bibliographic Details
Published inDifferential equations and dynamical systems Vol. 31; no. 1; pp. 93 - 111
Main Authors Mahrouf, Marouane, Lotfi, El Mehdi, Hattaf, Khalid, Yousfi, Noura
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.01.2023
Springer Nature B.V
Subjects
Computer Science
Dynamic programming
Engineering
Mathematics
Mathematics and Statistics
Maximum principle
Minimum cost
Optimal control
Optimization
Original Research
Pharmaceuticals
Optimal control theory
Stochastic differential equations (SDEs)
Epidemic models
Pontryagin’s Maximum Principle
HJB equation
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Summary:In this paper, we study an optimal control problem for a generalized stochastic SIVR model as well as for the corresponding deterministic model. We consider two control strategies in the optimal control model, namely: the successful practice of non-pharmaceutical interventions and vaccination for susceptible strategies. The existence of optimal control in the deterministic case is proved and it is solved by using Pontryagins Maximum Principle. Moreover, the stochastic optimal control problem is discussed by using Dynamic programming approach and the results are obtained numerically through simulation using an approximation based on the solution of the deterministic model. Outputs of the simulations show that our control strategies play important role in the minimization of infectious population with minimum cost.
ISSN:0971-3514
0974-6870
DOI:10.1007/s12591-020-00538-4