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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 |
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.
References:
[1] |
D. Burg, L. Rong, A. U. Neumann and H. Dahari,
Mathematical modeling of viral kinetics under immune control during primary HIV-1 infection,, Journal of Theoretical Biology, 259 (2009), 751-759.
doi: 10.1016/j.jtbi.2009.04.010. |
[2] |
P. V. Driessche and J. Watmough,
Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Mathematical Biosciences, 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[3] |
A. Dutta and P. K. Gupta,
A mathematical model for transmission dynamics of HIV/AIDS with effect of weak CD4+ T cells,, Chinese Journal of Physics, 56 (2018), 1045-1056.
|
[4] |
P. Essunger and A. S. Perelson,
Modeling HIV infection of CD4+ T-cell subpopulations,, Journal of Theoretical Biology, 170 (1994), 367-391.
|
[5] |
G. Haas, A. Hosmalin, F. Hadida, J. Duntze, P. Debré and B. Autran,
Dynamics of HIV variants and specific cytotoxic T-cell recognition in non-progressors and progressors,, Immunology Letter, 57 (1997), 63-68.
|
[6] |
H. F. Huo, R. Chen and X. Y. Wang,
Modelling and stability of HIV/AIDS epidemic model with treatment,, Applied Mathematical Modelling, 40 (2016), 6550-6559.
doi: 10.1016/j.apm.2016.01.054. |
[7] |
Y. Liu and C. Chen,
Role of nanotechnology in HIV/AIDS vaccine development,, Advanced Drug Delivery Reviews, 103 (2016), 76-89.
|
[8] |
J. Luo, W. Wang, H. Chen and R. Fu,
Bifurcations of a mathematical model for HIV dynamics,, Journal of Mathematical Analysis and Applications, 434 (2016), 837-857.
doi: 10.1016/j.jmaa.2015.09.048. |
[9] |
H. J. Marquez, Nonlinear Control Systems Analysis and Design, Wiley, 2003. |
[10] |
A. Mojaver and H. Kheiri,
Mathematical analysis of a class of HIV infection models of CD4+ T-cells with combined antiretroviral therapy,, Applied Mathematics and Computation, 259 (2015), 258-270.
doi: 10.1016/j.amc.2015.02.064. |
[11] |
L. Rong, M. A. Gilchrist, Z. Feng and A. S. Perelson,
Modeling within host HIV-1 dynamics and the evolution of drug resistance: Tradeoffs between viral enzyme function and drug susceptibility,, Journal of Theoretical Biology, 247 (2007), 804-818.
doi: 10.1016/j.jtbi.2007.04.014. |
[12] |
P. K. Srivastava and P. Chandra,
Modeling the dynamic of HIV and CD4+ T cells during primary infection,, Nonlinear Analysis: Real World Applications, 11 (2010), 612-618.
doi: 10.1016/j.nonrwa.2008.10.037. |
[13] |
S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, New York City: Springer Verlag, 2003. |
show all references
References:
[1] |
D. Burg, L. Rong, A. U. Neumann and H. Dahari,
Mathematical modeling of viral kinetics under immune control during primary HIV-1 infection,, Journal of Theoretical Biology, 259 (2009), 751-759.
doi: 10.1016/j.jtbi.2009.04.010. |
[2] |
P. V. Driessche and J. Watmough,
Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Mathematical Biosciences, 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[3] |
A. Dutta and P. K. Gupta,
A mathematical model for transmission dynamics of HIV/AIDS with effect of weak CD4+ T cells,, Chinese Journal of Physics, 56 (2018), 1045-1056.
|
[4] |
P. Essunger and A. S. Perelson,
Modeling HIV infection of CD4+ T-cell subpopulations,, Journal of Theoretical Biology, 170 (1994), 367-391.
|
[5] |
G. Haas, A. Hosmalin, F. Hadida, J. Duntze, P. Debré and B. Autran,
Dynamics of HIV variants and specific cytotoxic T-cell recognition in non-progressors and progressors,, Immunology Letter, 57 (1997), 63-68.
|
[6] |
H. F. Huo, R. Chen and X. Y. Wang,
Modelling and stability of HIV/AIDS epidemic model with treatment,, Applied Mathematical Modelling, 40 (2016), 6550-6559.
doi: 10.1016/j.apm.2016.01.054. |
[7] |
Y. Liu and C. Chen,
Role of nanotechnology in HIV/AIDS vaccine development,, Advanced Drug Delivery Reviews, 103 (2016), 76-89.
|
[8] |
J. Luo, W. Wang, H. Chen and R. Fu,
Bifurcations of a mathematical model for HIV dynamics,, Journal of Mathematical Analysis and Applications, 434 (2016), 837-857.
doi: 10.1016/j.jmaa.2015.09.048. |
[9] |
H. J. Marquez, Nonlinear Control Systems Analysis and Design, Wiley, 2003. |
[10] |
A. Mojaver and H. Kheiri,
Mathematical analysis of a class of HIV infection models of CD4+ T-cells with combined antiretroviral therapy,, Applied Mathematics and Computation, 259 (2015), 258-270.
doi: 10.1016/j.amc.2015.02.064. |
[11] |
L. Rong, M. A. Gilchrist, Z. Feng and A. S. Perelson,
Modeling within host HIV-1 dynamics and the evolution of drug resistance: Tradeoffs between viral enzyme function and drug susceptibility,, Journal of Theoretical Biology, 247 (2007), 804-818.
doi: 10.1016/j.jtbi.2007.04.014. |
[12] |
P. K. Srivastava and P. Chandra,
Modeling the dynamic of HIV and CD4+ T cells during primary infection,, Nonlinear Analysis: Real World Applications, 11 (2010), 612-618.
doi: 10.1016/j.nonrwa.2008.10.037. |
[13] |
S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, New York City: Springer Verlag, 2003. |


Parameters | Explanations |
r | Natural production rate of uninfected CD4+ T cells |
Fusion rate of CD4+ T-cells and virus | |
Rate of new infection into the infective compartment | |
Recovery rate of infected cells | |
Normal death rate of uninfected CD4+ T cells | |
Lytic death rate of infected cells | |
Loss rate of virus | |
Average number of viral particles produced by an | |
infected CD4+ T-cell |
Parameters | Explanations |
r | Natural production rate of uninfected CD4+ T cells |
Fusion rate of CD4+ T-cells and virus | |
Rate of new infection into the infective compartment | |
Recovery rate of infected cells | |
Normal death rate of uninfected CD4+ T cells | |
Lytic death rate of infected cells | |
Loss rate of virus | |
Average number of viral particles produced by an | |
infected CD4+ T-cell |
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