# American Institute of Mathematical Sciences

December  2019, 9(4): 393-399. doi: 10.3934/naco.2019038

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

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

* 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  August 2019

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

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.

Citation: Praveen Kumar Gupta, Ajoy Dutta. Numerical solution with analysis of HIV/AIDS dynamics model with effect of fusion and cure rate. Numerical Algebra, Control & Optimization, 2019, 9 (4) : 393-399. doi: 10.3934/naco.2019038
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##### References:
Dynamical behaviour of the model (1) for $R_0 = 0.9406 < 1$
Dynamical behaviour of the model (1) for $R_0 = 5.6140 > 1$
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
 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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