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Stability preserving NSFD scheme for a general virus dynamics model with antibody and cell-mediated responses

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  • Elaiw, A.M.
  • Alshaikh, M.A.

Abstract

Nonstandard finite difference (NSFD) is one of the efficient computational methods that has been used to discretize various viral infection models. In this paper we present a NSFD scheme for a virus dynamics model with antibody and cell-mediated responses. Two types of infected cells are incorporated into the model, namely latently infected and actively infected cells. The incidence rate of infection as well as the production and removal rates of all compartments are modeled by general nonlinear functions. We prove that NSFD preserves the positivity and boundedness of the solutions of the model. Based on four threshold parameters the existence of five equilibria is established. We perform global stability of all equilibria of the model by using Lyapunov approach. Numerical simulations are carried out to illustrate our theoretical results. A comparison between NSFD method and Runge-Kutta method is presented.

Suggested Citation

  • Elaiw, A.M. & Alshaikh, M.A., 2020. "Stability preserving NSFD scheme for a general virus dynamics model with antibody and cell-mediated responses," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920302629
    DOI: 10.1016/j.chaos.2020.109862
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    References listed on IDEAS

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    1. Elaiw, A.M. & Hobiny, A.D. & Al Agha, A.D., 2020. "Global dynamics of reaction-diffusion oncolytic M1 virotherapy with immune response," Applied Mathematics and Computation, Elsevier, vol. 367(C).
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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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