Optimal control of an epidemic model with a saturated incidence rate
Articles
Hassan Laarabi
Université Hassan II Mohammadia, Morocco
El Houssine Labriji
Université Hassan II Mohammadia, Morocco
Mostafa Rachik
Université Hassan II Mohammadia, Morocco
Abdelilah Kaddar
Université Mohammed V-Souissi, Morocco
Published 2012-10-25
https://doi.org/10.15388/NA.17.4.14050
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Keywords

SIR model
optimal control
vaccination

How to Cite

Laarabi H., Labriji E. H., Rachik M. and Kaddar A. (2012) “Optimal control of an epidemic model with a saturated incidence rate”, Nonlinear Analysis: Modelling and Control, 17(4), pp. 448-459. doi: 10.15388/NA.17.4.14050.

Abstract

In this study we consider a mathematical model of an SIR epidemic model with a saturated incidence rate. We used the optimal vaccination strategies to minimize the susceptible and infected individuals and to maximize the number of recovered individuals. We work in the nonlinear optimal control framework. The existence result was discussed. A characterization of the optimal control via adjoint variables was established. We obtained an optimality system that we sought to solve numerically by a competitive Gauss–Seidel like implicit difference method.

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