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Presentation of Malaria Epidemics Using Multiple Optimal Controls

Author

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

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.

Suggested Citation

  • Abid Ali Lashari & Shaban Aly & Khalid Hattaf & Gul Zaman & Il Hyo Jung & Xue-Zhi Li, 2012. "Presentation of Malaria Epidemics Using Multiple Optimal Controls," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, June.
    • Handle: RePEc:hin:jnljam:946504
    DOI: 10.1155/2012/946504
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    Cited by:

    1. Samson Olaniyi & Olusegun A. Ajala & Sulaimon F. Abimbade, 2023. "Optimal Control Analysis of a Mathematical Model for Recurrent Malaria Dynamics," SN Operations Research Forum, Springer, vol. 4(1), pages 1-24, March.
    2. Hasan, Bushra & Singh, Manmohan & Richards, David & Blicblau, Aaron, 2019. "Mathematical modelling of Zika virus as a mosquito-borne and sexually transmitted disease with diffusion effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 56-75.
    3. Kuddus, Md Abdul & Rahman, Azizur, 2022. "Modelling and analysis of human–mosquito malaria transmission dynamics in Bangladesh," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 123-138.
    4. Mandal, Parna & Faragó, István, 2021. "Operator splitting and error analysis in malaria modeling," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    5. Fahad Al Basir & Teklebirhan Abraha, 2023. "Mathematical Modelling and Optimal Control of Malaria Using Awareness-Based Interventions," Mathematics, MDPI, vol. 11(7), pages 1-25, March.
    6. Xue, Leilei & Sun, Liping & Guo, Songbai, 2023. "Dynamic effects of asymptomatic infections on malaria transmission," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 172-182.

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