Dynamical behavior of HIV immunology model with non-integer time fractional derivatives

Abstract

This paper introduces a mathematical model which describes the dynamics of the spread of HIV in the human body. Human immunodeficiency virus infection destroys the body immune system, increases the risk of certain pathologies, damages body organs such as the brain, kidney and heart or cause the death. Unfortunately, this infection disease currently has no cure to control the diseases. We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV) infection. The Caputo fractional derivative operator of order ∈ (0,1] is employed to obtain the system of fractional differential equations. The basic reproductive number is derived for a general viral production rate which determines the local stability of the infection free equilibrium. The solution of the time fractional model has been procured by employing Laplace Adomian decomposition method (LADM) and the accuracy of the scheme is presented by convergence analysis Moreover, numerical simulation are performed to study the dynamical behavior of solution of the models. Simulations of different epidemiological classes at the effect of the fractional parameters revealed that most undergoing treatment join the recovered class. The results show the both viral production rate and death rate of infected cells play an important role the disease in the society.

Analysis and dynamical behavior of fractional‐order cancer model with vaccine strategy

“…Fractional-order models are more convincing and useful than the classical-order models. 11,12 Laplace transform methodology could be a helpful technique in numerous fields of life science, engineering, and math. The coupling of ADM and astronomer Pierre Simon de Laplace transformation leads to a study methodology noted as Laplace Adomain decomposition method.…”

“…The outlines memory and transmitted properties of various mathematical models are the well‐known features of fractional differential equations. Fractional‐order models are more convincing and useful than the classical‐order models …”

Mathematical Analysis of Fractional Order Co-Infection TB and HIV Model

“…Fractional order derivative produces greater degree of freedom in these models. Arbitrary order derivatives are powerful tools for the discretion of the dynamical behavior of various biomaterial and systems [16,17].…”

Dynamical Behavior of Fractional Order SVIR Epidemic Model

“…Fractional order derivative produces greater degree of freedom in these models. Arbitrary order derivatives are powerful tools for the discretion of the dynamical behavior of various biomaterial and systems [19,20].…”