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Treatment of HIV/AIDS epidemic model with vertical transmission by using evolutionary Padé-approximation

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  • Tabassum, Muhammad Farhan
  • Saeed, Muhammad
  • Akgül, Ali
  • Farman, Muhammad
  • Chaudhry, Nazir Ahmad

Abstract

Human Immunodeficiency Virus (HIV) infection has become a significant infectious disease for both developed and developing countries that can contribute to the acquired immunodeficiency syndrome (AIDS). In this study a nonlinear mathematical model for the transmission of HIV/AIDS has been proposed and discussed in a populace of changing size with transfer of infection. The theorems and propositions have been constructed for well-posed-ness and bounded-ness of the model respectively. Evolutionary Padé-approximation (EPA) technique has been used for the treatment of this nonlinear mathematical model. Initial conditions are converted into constraints and constraints’ problem is transformed into unconstrained by using penalty function. In the suggested EPA method, no step lengths have to be chosen, also converges to a steady state point is proved. The model for the transmission of HIV/AIDS also solved by using non-standard finite difference (NSFD) scheme and results were compared, simulations justify our outcomes more efficient and compact. Finally, a convergence and error analysis evidence that the convergence speed of EPA is superior that of the NSFD.

Suggested Citation

  • Tabassum, Muhammad Farhan & Saeed, Muhammad & Akgül, Ali & Farman, Muhammad & Chaudhry, Nazir Ahmad, 2020. "Treatment of HIV/AIDS epidemic model with vertical transmission by using evolutionary Padé-approximation," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    • Handle: RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920300886
    DOI: 10.1016/j.chaos.2020.109686
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    References listed on IDEAS

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    1. Singh, Jagdev & Kumar, Devendra & Baleanu, Dumitru & Rathore, Sushila, 2018. "An efficient numerical algorithm for the fractional Drinfeld–Sokolov–Wilson equation," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 12-24.
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    Cited by:

    1. Goyal, Manish & Baskonus, Haci Mehmet & Prakash, Amit, 2020. "Regarding new positive, bounded and convergent numerical solution of nonlinear time fractional HIV/AIDS transmission model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Xu, Changjin & Alhejaili, Weaam & Saifullah, Sayed & Khan, Arshad & Khan, Javed & El-Shorbagy, M.A., 2022. "Analysis of Huanglongbing disease model with a novel fractional piecewise approach," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Selvan, T. Tamil & Kumar, M., 2023. "Dynamics of a deterministic and a stochastic epidemic model combined with two distinct transmission mechanisms and saturated incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).

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