Study of the Fractional-Order HIV-1 Infection Model with Uncertainty in Initial Data

Yong Wu,Kamal Shah,Aman Ullah,Shabir Ahmad,Nasser Hassen Sweilam

doi:10.1155/2022/7286460

Yong Wu, Kamal Shah + Show 3 more

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https://doi.org/10.1155/2022/7286460

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Abstract

Uncertainty always lives with us. We cannot take exact measurement of initial conditions or parameters values in a mathematical model. As humans, we are remaining alive in an environment where the uncertainties lie in the modelling of physical phenomena. There might be some incomplete information or estimation of the parameter or initial values. To handle uncertainty, we use fuzzy operators rather than classical operators. In this paper, we study a model of HIV-1 infection by taking uncertainty in the initial data under Caputo fractional operator. We explore the existence and uniqueness of the results through fixed-point theory. We study the Ulam–Hyres stability of the considered model. By using the fuzzy Laplace Adomian decomposition method, numerical results are obtained for specific fuzzy initial conditions. To better understand the behaviour of the fuzzy solution, we present the obtained numerical results graphically for various fractional orders where the uncertainty lies in [0, 1].

Highlights

IntroductionAIDS (acquired immune deficiency syndrome) is one of the most dangerous diseases caused by a pathogen virus called HIV (human immunodeficiency virus) and leads a person to death
AIDS is one of the most dangerous diseases caused by a pathogen virus called HIV and leads a person to death
Many researchers have investigated the dynamics of HIV infection models [1,2,3]

Summary

Introduction

AIDS (acquired immune deficiency syndrome) is one of the most dangerous diseases caused by a pathogen virus called HIV (human immunodeficiency virus) and leads a person to death. At the end of 2019, about 38 million people, identified by the WHO (World Health Organization), were surviving with HIV. In 2019, 0.69 million people died from diseases associated with AIDS. Many researchers have investigated the dynamics of HIV infection models [1,2,3]. A lot of methods have been used by researchers to find a solution to HIV infections [4,5,6]. In [7], the authors presented an HIV-1 infection model which contains five compartments, denoted by M (t) (the uninfected CD4+ T cells), M ∗(t) (the concentration of infected cells), M ∗∗(t) (the concentration of double cells), and Vp(t) and Vr(t) (the densities of pathogen viruses), respectively. In [7], the authors presented an HIV-1 infection model which contains five compartments, denoted by M (t) (the uninfected CD4+ T cells), M ∗(t) (the concentration of infected cells), M ∗∗(t) (the concentration of double cells), and Vp(t) and Vr(t) (the densities of pathogen viruses), respectively. e integer-order model of HIV-1 infection is given by

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