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Structure Preserving Numerical Analysis of HIV and CD4+T-Cells Reaction Diffusion Model in Two Space Dimensions

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  • Ahmed, Nauman
  • Rafiq, Muhammad
  • Adel, Waleed
  • Rezazadeh, Hadi
  • Khan, Ilyas
  • Nisar, Kottakkaran Sooppy

Abstract

In this paper, a new HIV CD4+T cells reaction-diffusion model in two dimensions has been introduced. Two novel and efficient positivity preserving finite difference schemes for the numerical solution has been used. The positivity property is of great importance in epidemic models because negative values have no meaning. The stability and consistency of the proposed positivity preserving schemes have been discussed briefly. A comparison of the proposed schemes with an extensively used Euler scheme has been provided. The numerical simulations of all the schemes have been presented with the help of a numerical test and found that the Euler method shows false behavior which is not a part of the continuous system. Moreover, both proposed positivity preserving schemes illustrate the behavior which is consistent with the continuous system.

Suggested Citation

  • Ahmed, Nauman & Rafiq, Muhammad & Adel, Waleed & Rezazadeh, Hadi & Khan, Ilyas & Nisar, Kottakkaran Sooppy, 2020. "Structure Preserving Numerical Analysis of HIV and CD4+T-Cells Reaction Diffusion Model in Two Space Dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920307037
    DOI: 10.1016/j.chaos.2020.110307
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    References listed on IDEAS

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    1. Jajarmi, Amin & Arshad, Sadia & Baleanu, Dumitru, 2019. "A new fractional modelling and control strategy for the outbreak of dengue fever," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    2. Hajipour, Mojtaba & Jajarmi, Amin & Malek, Alaeddin & Baleanu, Dumitru, 2018. "Positivity-preserving sixth-order implicit finite difference weighted essentially non-oscillatory scheme for the nonlinear heat equation," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 146-158.
    3. Xiaoting Fan & Yi Song & Wencai Zhao, 2018. "Modeling Cell-to-Cell Spread of HIV-1 with Nonlocal Infections," Complexity, Hindawi, vol. 2018, pages 1-10, August.
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    Cited by:

    1. Pasha, Syed Ahmed & Nawaz, Yasir & Arif, Muhammad Shoaib, 2023. "On the nonstandard finite difference method for reaction–diffusion models," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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