TY - JOUR
T1 - Dynamics Analysis of HIV-1 Infection Model with CTL Immune Response and Delays
AU - Guo , Ting
AU - Zhao , Fei
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 560
EP - 586
PY - 2024
DA - 2024/06
SN - 21
DO - http://doi.org/10.4208/ijnam2024-1022
UR - https://global-sci.org/intro/article_detail/ijnam/23202.html
KW - HIV-1, Delays, Stability, Hopf bifurcation, Lyapunov functionals.
AB - <p style="text-align: justify;">In this paper, we rigorously analyze an HIV-1 infection model with CTL immune
response and three time delays which represent the latent period, virus production period and
immune response delay, respectively. We begin this model with proving the positivity and boundedness of the solution. For this model, the basic reproduction number $R_0$ and the immune
reproduction number $R_1$ are identified. Moreover, we have shown that the model has three equilibria, namely the infection-free equilibrium $E_0,$ the infectious equilibrium without immune
response $E_1$ and the infectious equilibrium with immune response $E_2.$ By applying fluctuation
lemma and Lyapunov functionals, we have demonstrated that the global stability of $E_0$ and $E_1$ are only related to $R_0$ and $R_1.$ The local stability of the third equilibrium is obtained under four
situations. Further, we give the conditions for the existence of Hopf bifurcation. Finally, some
numerical simulations are carried out for illustrating the theoretical results.</p>