Investigation of fractal-fractional HIV infection by evaluating the drug therapy effect in the Atangana-Baleanu sense

Math Biosci Eng. 2022 Jul 28;19(11):10762-10808. doi: 10.3934/mbe.2022504.

Abstract

In this paper, we apply the fractal-fractional derivative in the Atangana-Baleanu sense to a model of the human immunodeficiency virus infection of CD$ 4^{+} $ T-cells in the presence of a reverse transcriptase inhibitor, which occurs before the infected cell begins producing the virus. The existence and uniqueness results obtained by applying Banach-type and Leray-Schauder-type fixed-point theorems for the solution of the suggested model are established. Stability analysis in the context of Ulam's stability and its various types are investigated in order to ensure that a close exact solution exists. Additionally, the equilibrium points and their stability are analyzed by using the basic reproduction number. Three numerical algorithms are provided to illustrate the approximate solutions by using the Newton polynomial approach, the Adam-Bashforth method and the predictor-corrector technique, and a comparison between them is presented. Furthermore, we present the results of numerical simulations in the form of graphical figures corresponding to different fractal dimensions and fractional orders between zero and one. We analyze the behavior of the considered model for the provided values of input factors. As a result, the behavior of the system was predicted for various fractal dimensions and fractional orders, which revealed that slight changes in the fractal dimensions and fractional orders had no impact on the function's behavior in general but only occur in the numerical simulations.

Keywords: HIV mathematical model; Ulam-Hyers stability; fixed point theorems; fractal-fractional operators; numerical scheme.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms
  • Basic Reproduction Number
  • Fractals*
  • HIV Infections* / drug therapy
  • Humans
  • Reverse Transcriptase Inhibitors

Substances

  • Reverse Transcriptase Inhibitors