Asian Journal of Pharmaceutical Research and Health Care

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A Study on an HIV Pathogenesis Model with Different Growth rates of Uninfected and Infected CD4+T cells


Affiliations
1 Department of Mathematics, Barnagar College, Sorbhog – 781317, Barpeta, Assam, India
2 Department of Mathematics, Gauhati University, Guwahati – 781014, Assam, India
 

The objective of this paper is to discuss the dynamics of an HIV pathogenesis model with full logistic target cell growth of uninfected T cells and cure rate of infected T cells. Local and global dynamics of both infection-free and infected equilibrium points are rigorously established. It is found that if basic reproduction number R0≤1, the infection is cleared from T cells and if R0>1, the HIV infection persists. Also, we have carried out numerical simulations to verify the results. The existence of non-trivial periodic solution is also studied by means of numerical simulation. Therefore, we find a parameter region where infected equilibrium point is globally stable to make the model biologically significant. From the overall study, it is found that proliferation of T cells cannot be ignored during the study of HIV dynamics for better results and we can focus on a treatment policy which can control the parameters of the model in such a way that the basic reproduction number remains less than or equal to one.


Keywords

HIV, Local and Global Stability, Periodic Solution, Treatment

2010 AMS classification: 34A34, 34D23, 37C25

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  • A Study on an HIV Pathogenesis Model with Different Growth rates of Uninfected and Infected CD4+T cells

Abstract Views: 424  |  PDF Views: 166

Authors

Bhagya Jyoti Nath
Department of Mathematics, Barnagar College, Sorbhog – 781317, Barpeta, Assam, India
Kaushik Dehingia
Department of Mathematics, Gauhati University, Guwahati – 781014, Assam, India
Hemanta Kumar Sarmah
Department of Mathematics, Gauhati University, Guwahati – 781014, Assam, India

Abstract


The objective of this paper is to discuss the dynamics of an HIV pathogenesis model with full logistic target cell growth of uninfected T cells and cure rate of infected T cells. Local and global dynamics of both infection-free and infected equilibrium points are rigorously established. It is found that if basic reproduction number R0≤1, the infection is cleared from T cells and if R0>1, the HIV infection persists. Also, we have carried out numerical simulations to verify the results. The existence of non-trivial periodic solution is also studied by means of numerical simulation. Therefore, we find a parameter region where infected equilibrium point is globally stable to make the model biologically significant. From the overall study, it is found that proliferation of T cells cannot be ignored during the study of HIV dynamics for better results and we can focus on a treatment policy which can control the parameters of the model in such a way that the basic reproduction number remains less than or equal to one.


Keywords


HIV, Local and Global Stability, Periodic Solution, Treatment

2010 AMS classification: 34A34, 34D23, 37C25


References





DOI: https://doi.org/10.18311/ajprhc%2F2020%2F25775