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Dynamical Strategy to Control the Accuracy of the Nonlinear Bio-Mathematical Model of Malaria Infection

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  • Samad Noeiaghdam

    (Department of Applied Mathematics and Programming, South Ural State University, Lenin Prospect 76, 454080 Chelyabinsk, Russia
    Industrial Mathematics Laboratory, Baikal School of BRICS, Irkutsk National Research Technical University, 664074 Irkutsk, Russia)

  • Sanda Micula

    (Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania)

Abstract

This study focuses on solving the nonlinear bio-mathematical model of malaria infection. For this aim, the HATM is applied since it performs better than other methods. The convergence theorem is proven to show the capabilities of this method. Instead of applying the FPA, the CESTAC method and the CADNA library are used, which are based on the DSA. Applying this method, we will be able to control the accuracy of the results obtained from the HATM. Also the optimal results and the numerical instabilities of the HATM can be obtained. In the CESTAC method, instead of applying the traditional absolute error to show the accuracy, we use a novel condition and the CESTAC main theorem allows us to do that. Plotting several ℏ -curves the regions of convergence are demonstrated. The numerical approximations are obtained based on both arithmetics.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:1031-:d:547987
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    References listed on IDEAS

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    1. Vignes, J., 1993. "A stochastic arithmetic for reliable scientific computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(3), pages 233-261.
    2. Naik, Parvaiz Ahmad & Zu, Jian & Ghoreishi, Mohammad, 2020. "Estimating the approximate analytical solution of HIV viral dynamic model by using homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Naik, Parvaiz Ahmad & Owolabi, Kolade M. & Yavuz, Mehmet & Zu, Jian, 2020. "Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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    2. 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.

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