IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i7p1687-d1113342.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/7/1687/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/7/1687/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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).
    3. 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.
    4. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Agrawal, Khushbu & Kumar, Ranbir & Kumar, Sunil & Hadid, Samir & Momani, Shaher, 2022. "Bernoulli wavelet method for non-linear fractional Glucose–Insulin regulatory dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. 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.
    4. Mandal, Parna & Faragó, István, 2021. "Operator splitting and error analysis in malaria modeling," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    5. Sharbayta, Sileshi Sintayehu & Buonomo, Bruno & d'Onofrio, Alberto & Abdi, Tadesse, 2022. "‘Period doubling’ induced by optimal control in a behavioral SIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    6. Abraha, Teklebirhan & Al Basir, Fahad & Obsu, Legesse Lemecha & Torres, Delfim F.M., 2021. "Pest control using farming awareness: Impact of time delays and optimal use of biopesticides," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    7. 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).
    8. Yuan, Yiran & Li, Ning, 2022. "Optimal control and cost-effectiveness analysis for a COVID-19 model with individual protection awareness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    9. Jin, Xihua & Jia, Jianwen, 2020. "Qualitative study of a stochastic SIRS epidemic model with information intervention," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    10. Kimberly M. Thompson, 2017. "Modeling and Managing the Risks of Measles and Rubella: A Global Perspective Part II," Risk Analysis, John Wiley & Sons, vol. 37(6), pages 1041-1051, June.
    11. Jamie Guth & Marie Lamy & Nikhil Murali & Patil Pankaj & Yongyuth Yuthavong, 2022. "Meeting malaria elimination targets and remaining challenges: Qualitative research on perceptions of stakeholders in India and Southeast Asia," Asia and the Pacific Policy Studies, Wiley Blackwell, vol. 9(2), pages 178-195, May.
    12. Deng, Yang & He, Daihai & Zhao, Yi, 2024. "The impacts of anti-protective awareness and protective awareness programs on COVID-19 outbreaks," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    13. 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.
    14. Sulaimon F. Abimbade & Furaha M. Chuma & Sunday O. Sangoniyi & Ramoshweu S. Lebelo & Kazeem O. Okosun & Samson Olaniyi, 2024. "Global Dynamics of a Social Hierarchy-Stratified Malaria Model: Insight from Fractional Calculus," Mathematics, MDPI, vol. 12(10), pages 1-19, May.
    15. Ray, Santanu & Basir, Fahad Al, 2020. "Impact of incubation delay in plant–vector interaction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 16-31.
    16. 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.
    17. Edwin Ochieng Okul & Raphael Ondeko Nyonje, 2020. "Examining stakeholder involvement in the evaluation process for program improvement," International Journal of Research in Business and Social Science (2147-4478), Center for the Strategic Studies in Business and Finance, vol. 9(5), pages 179-191, September.
    18. Konstantinos Mitsakakis & Sebastian Hin & Pie Müller & Nadja Wipf & Edward Thomsen & Michael Coleman & Roland Zengerle & John Vontas & Konstantinos Mavridis, 2018. "Converging Human and Malaria Vector Diagnostics with Data Management towards an Integrated Holistic One Health Approach," IJERPH, MDPI, vol. 15(2), pages 1-26, February.
    19. Lorenzo Cáceres Carrera & Carlos Victoria & Jose L Ramirez & Carmela Jackman & José E Calzada & Rolando Torres, 2019. "Study of the epidemiological behavior of malaria in the Darien Region, Panama. 2015–2017," PLOS ONE, Public Library of Science, vol. 14(11), pages 1-30, November.
    20. Bethencourt, Carlos & Marrero, Gustavo A. & Ngoudji, Charlie Y., 2021. "The Fight against Malaria: A New Index for Quantifying and Assessing Policy Implementation Actions to Reduce Mortality in Sub-Saharan Africa," MPRA Paper 108570, University Library of Munich, Germany.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1687-:d:1113342. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.