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Mathematical Modelling and Optimal Control of Malaria Using Awareness-Based Interventions

Author

Listed:
  • Fahad Al Basir

    (Department of Mathematics, Asansol Girls’ College, Asansol 713304, West Bengal, India
    These authors contributed equally to this work.)

  • Teklebirhan Abraha

    (Department of Mathematics, Addis Ababa Science and Technology University, Addis Ababa P.O. Box 16417, Ethiopia
    Department of Mathematics, Aksum University, Aksum P.O. Box 1010, Ethiopia
    These authors contributed equally to this work.)

Abstract

Malaria is a serious illness caused by a parasite, called Plasmodium, transmitted to humans through the bites of female Anopheles mosquitoes. The parasite infects and destroys the red blood cells in the human body leading to symptoms, such as fever, headache, and flu-like illness. Awareness campaigns that educate people about malaria prevention and control reduce transmission of the disease. In this research, a mathematical model is proposed to study the impact of awareness-based control measures on the transmission dynamics of malaria. Some basic properties of the proposed model, such as non-negativity and boundedness of the solutions, the existence of the equilibrium points, and their stability properties, have been studied using qualitative theory. Disease-free equilibrium is globally asymptotic when the basic reproduction number, R 0 , is less than the number of current cases. Finally, optimal control theory is applied to minimize the cost of disease control and solve the optimal control problem by applying Pontryagin’s minimum principle. Numerical simulations have been provided for the confirmation of the analytical results. Endemic equilibrium exists for R 0 > 1 , and a forward transcritical bifurcation occurs at R 0 = 1 . The optimal profiles of the treatment process, organizing awareness campaigns, and insecticide uses are obtained for the cost-effectiveness of malaria management. This research concludes that awareness campaigns through social media with an optimal control approach are best for cost-effective malaria management.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1687-:d:1113342
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    References listed on IDEAS

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    1. José A Nájera & Matiana González-Silva & Pedro L Alonso, 2011. "Some Lessons for the Future from the Global Malaria Eradication Programme (1955–1969)," PLOS Medicine, Public Library of Science, vol. 8(1), pages 1-7, January.
    2. Basir, Fahad Al & Ray, Santanu & Venturino, Ezio, 2018. "Role of media coverage and delay in controlling infectious diseases: A mathematical model," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 372-385.
    3. Ndii, Meksianis Z. & Adi, Yudi Ari, 2021. "Understanding the effects of individual awareness and vector controls on malaria transmission dynamics using multiple optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    4. 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.
    5. Malik Muhammad Ibrahim & Muhammad Ahmad Kamran & Malik Muhammad Naeem Mannan & Sangil Kim & Il Hyo Jung, 2020. "Impact of Awareness to Control Malaria Disease: A Mathematical Modeling Approach," Complexity, Hindawi, vol. 2020, pages 1-13, October.
    6. Samad Noeiaghdam & Sanda Micula, 2021. "Dynamical Strategy to Control the Accuracy of the Nonlinear Bio-Mathematical Model of Malaria Infection," Mathematics, MDPI, vol. 9(9), pages 1-24, May.
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    Cited by:

    1. Azhar Iqbal Kashif Butt & Muhammad Imran & Brett A. McKinney & Saira Batool & Hassan Aftab, 2023. "Mathematical and Stability Analysis of Dengue–Malaria Co-Infection with Disease Control Strategies," Mathematics, MDPI, vol. 11(22), pages 1-28, November.

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