Understanding role of CTL cells and antibodies on a delayed HIV mathematical model: A dynamical analysis

  • Mamta Barik
  • Sudipa Chauhan Amity Institute of Applied Science, Amity University, Noida
  • Sumit Kaur Bhatia
  • Om Prakash Misra


This paper is mainly concerned with an investigation of a delayed mathematical model with adaptive immunity. Several mathematical models have been introduced in the literature in order to gain insights into the dynamics of the disease progression, however, the results considering the effect of multiple factors which include antigen-driven CD4 T-cell, delay, activation of CTL’s response during the infection process are not involved. Further, the global stability analysis of equilibrium point through geometrical approach is also a new advanced method not discussed yet. Hence, this paper encapsulates the analysis of role of immunity on the dynamics of a delayed HIV model which involves CTL cells and antibodies in the initial stage of HIV. The boundedness, existence of boundary and interior equilibrium points have been obtained. We would be defining new thresholds R0, R1, R2, R3 on which the local stability of the boundary and interior equilibrium points depends. Therefore, the overall contribution of the paper is listed as follows: (1) construction of a non-linear delay mathematical model, (2) local stability of the steady state solutions derived based on thresholds; (3) global stability of equilibrium point with immunity by geometrical approach (4) numerical simulation and sensitivity analysis based on all the parameters is performed to validate the effectiveness and applicability of the theoretical predictions and Finally, global sensitivity analysis of thresholds R2, R3 are done using Latin hypercube sampling scheme(LHS). These thresholds are significant as they are associated to antibodies and CTL cells which would give a deep insight of the sensitive parameters required to suppress the infection.