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


Affiliations

  • Barnagar College, Sorbhog, Department of Mathematics, Assam, 781317, India
  • Gauhati University, Department of Mathematics, Guwahati, Assam, 781014, 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


Subject Discipline

Mathematics

Full Text:

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