Existence theory and numerical simulation of HIV-I cure model with new fractional derivative possessing a non-singular kernel

Abstract

In this research work, a mathematical model related to HIV-I cure infection therapy consisting of three populations is investigated from the fractional calculus viewpoint. Fractional version of the model under consideration has been proposed. The proposed model is examined by using the Atangana-Baleanu fractional operator in the Caputo sense (ABC). The theory of Picard-Lindelöf has been employed to prove existence and uniqueness of the special solutions of the proposed fractional-order model. Further, it is also shown that the non-negative hyper-plane R 3 + is a positively invariant region for the underlying model. Finally, to analyze the results, some numerical simulations are carried out via a numerical technique recently devised for finding approximate solutions of fractional-order dynamical systems. Upon comparison of the numerical simulations, it has been demonstrated that the proposed fractional-order model is more accurate than its classical version. All the necessary computations have been performed using MATLAB R2018a with double precision arithmetic.

A finite-difference discretization preserving the structure of solutions of a diffusive model of type-1 human immunodeficiency virus

“…Some of these models are based on ordinary differential equations, and their analytical study is followed by simulation experiments which assess the validity of the qualitative results. To that end, various numerical methodologies have been designed and analyzed, like some algorithms for simulating the HIV-1 dynamics at a cellular level [6], stem cells therapy of HIV-1 infections [7], fractional optimal control problems on HIV-1 infection of CD4 + T cells using Legendre spectral collocation [8], HIV-1 cure models with fractional derivatives which possess a nonsingular kernel [9], stochastic HIV-1/AIDS epidemic models in two-sex populations [10], among other reports [5,[11][12][13].…”

“…Notice that system (2) is an integer-order diffusive extension of some HIV-1 propagation models available in the literature [9,14]. The use of such a system is due to the current information available of the mechanisms of CD4 + T cells and free HIV-1 infection particles in the blood.…”

Analytical Solutions for Nonlinear Dispersive Physical Model

“…e differential model has a broad application in many phenomena as in [12][13][14]. Recently, nonlinear fractional differential equations (NLFDEs) show significantly in engineering and applications of other sciences, for example, electrochemistry, physics, electromagnetics, and signal data processing [15][16][17][18][19][20][21][22].…”

An Operational Matrix Method Based on Poly-Bernoulli Polynomials for Solving Fractional Delay Differential Equations

“…These derivatives include the Caputo-Fabrizio [1] and Atangana-Baleanu fractional derivatives [2]. These new definitions have been applied in many areas, including the groundwater flow within a confined aquifer [3], the magnetohydrodynamic electroosmotic flow of Maxwell fluids [4], the modeling of a financial system [5,6], the modeling of various types of diseases or epidemics [7][8][9] and many other fields [10,11].…”