Journal of Applied Mathematics

Presentation of Malaria Epidemics Using Multiple Optimal Controls

Abid Ali Lashari, Shaban Aly, Khalid Hattaf, Gul Zaman, Il Hyo Jung, and Xue-Zhi Li

Full-text: Open access

Abstract

An existing model is extended to assess the impact of some antimalaria control measures, by re-formulating the model as an optimal control problem. This paper investigates the fundamental role of three type of controls, personal protection, treatment, and mosquito reduction strategies in controlling the malaria. We work in the nonlinear optimal control framework. The existence and the uniqueness results of the solution are discussed. A characterization of the optimal control via adjoint variables is established. The optimality system is solved numerically by a competitive Gauss-Seidel-like implicit difference method. Finally, numerical simulations of the optimal control problem, using a set of reasonable parameter values, are carried out to investigate the effectiveness of the proposed control measures.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 946504, 17 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495171

Digital Object Identifier
doi:10.1155/2012/946504

Mathematical Reviews number (MathSciNet)
MR2935539

Zentralblatt MATH identifier
1244.93111

Citation

Lashari, Abid Ali; Aly, Shaban; Hattaf, Khalid; Zaman, Gul; Jung, Il Hyo; Li, Xue-Zhi. Presentation of Malaria Epidemics Using Multiple Optimal Controls. J. Appl. Math. 2012 (2012), Article ID 946504, 17 pages. doi:10.1155/2012/946504. https://projecteuclid.org/euclid.jam/1355495171


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