Numerical solution with analysis of HIV/AIDS dynamics model with effect of fusion and cure rate

Praveen Kumar Gupta; Ajoy Dutta

doi:10.3934/naco.2019038

Article Contents

2019, Volume 9, Issue 4: 393-399. Doi: 10.3934/naco.2019038

This issue Previous Article Next Article Conformal deformations of a specific class of lorentzian manifolds with non-irreducible holonomy representation

Numerical solution with analysis of HIV/AIDS dynamics model with effect of fusion and cure rate

Praveen Kumar Gupta^, and
Ajoy Dutta

Department of Mathematics, National Institute of Technology Silchar, Cachar, Assam-788010, INDIA

^* Corresponding author: pkguptaitbhu@gmail.com
^* Corresponding author: pkguptaitbhu@gmail.com

The reviewing process of the paper is handled by Gafurjan Ibragimov, Siti Hasana Sapar and Siti Nur Iqmal Ibrahim

Received: December 2017

Revised: July 2018

Published online: August 2019

The first author is supported by Science, Technology & Innovation Scheme and CPDA grant.

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Abstract

The main objective of this manuscript is to study the dynamical behaviour and numerical solution of a HIV/AIDS dynamics model with fusion effect and cure rate. Local and global asymptotic stability of the model is established by Routh-Hurwitz criterion and Lyapunov functional method for infection-free equilibrium point. The numerical solutions of the model has also examined for support of analysis, through Mathematica software.

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Mathematics Subject Classification: Primary: 00A71, 34D20, 37N25; Secondary: 65L07.

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Figure 1. Dynamical behaviour of the model (1) for $ R_0 = 0.9406 < 1 $

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Figure 2. Dynamical behaviour of the model (1) for $ R_0 = 5.6140 > 1 $

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Table 1. List of parameters

Parameters	Explanations
r	Natural production rate of uninfected CD4+ T cells
$ \rho_1 $	Fusion rate of CD4+ T-cells and virus
$ \rho_2 $	Rate of new infection into the infective compartment
$ \rho_3 $	Recovery rate of infected cells
$ \sigma_1 $	Normal death rate of uninfected CD4+ T cells
$ \sigma_2 $	Lytic death rate of infected cells
$ \sigma_3 $	Loss rate of virus
$ A $	Average number of viral particles produced by an
	infected CD4+ T-cell

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