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Modeling the Impact of Human Awareness and Insecticide Use on Malaria Control: A Fractional-Order Approach

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  • Mlyashimbi Helikumi

    (Department of Mathematics and Statistics, College of Science and Technical Education, Mbeya University of Science and Technology, Mbeya P.O. Box 131, Tanzania)

  • Thobias Bisaga

    (Department of Mathematics and Statistics, College of Science and Technical Education, Mbeya University of Science and Technology, Mbeya P.O. Box 131, Tanzania)

  • Kimulu Ancent Makau

    (Department of Mathematics and Statistics, Machakos University, Machakos P.O. Box 136-90100, Kenya)

  • Adquate Mhlanga

    (The Program for Experimental and Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Chicago, Maywood, IL 84101, USA)

Abstract

In this research work, we developed a fractional-order model for the transmission dynamics of malaria, incorporating two control strategies: health education campaigns and the use of insecticides. The theoretical analysis of the model is presented, including the computation of disease-free equilibrium and basic reproduction number. We analyzed the stability of the proposed model using a well-formulated Lyapunov function. Furthermore, model parameter estimation was carried out using real data from malaria cases reported in Zimbabwe. We found that the fractional-order model provided a better fit to the real data compared to the classical integer-order model. Sensitivity analysis of the basic reproduction number was performed using computed partial rank correlation coefficients to assess the effect of each parameter on malaria transmission. Additionally, we conducted numerical simulations to evaluate the impact of memory effects on the spread of malaria. The simulation results indicated that the order of derivatives significantly influences the dynamics of malaria transmission. Moreover, we simulated the model to assess the effectiveness of the proposed control strategies. Overall, the interventions were found to have the potential to significantly reduce the spread of malaria within the population.

Suggested Citation

  • Mlyashimbi Helikumi & Thobias Bisaga & Kimulu Ancent Makau & Adquate Mhlanga, 2024. "Modeling the Impact of Human Awareness and Insecticide Use on Malaria Control: A Fractional-Order Approach," Mathematics, MDPI, vol. 12(22), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3607-:d:1524053
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    References listed on IDEAS

    as
    1. A. Mhlanga & C. P. Bhunu & S. Mushayabasa, 2014. "HSV-2 and Substance Abuse amongst Adolescents: Insights through Mathematical Modelling," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-17, November.
    2. 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.
    3. William Atokolo & Godwin Mbah Christopher Ezike, 2020. "Modeling the Control of Zika Virus Vector Population Using the Sterile Insect Technology," Journal of Applied Mathematics, Hindawi, vol. 2020, pages 1-12, September.
    4. Ghanbari, Behzad & Atangana, Abdon, 2020. "A new application of fractional Atangana–Baleanu derivatives: Designing ABC-fractional masks in image processing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
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