STABILITY AND HOPF BIFURCATION ANALYSIS OF A HTLV-I INFECTION MODEL WITH TIME-DELAY CTL IMMUNE RESPONSE

. This paper is devoted to proposing a mathematical model in order to explore the dynamics of HTLV-I (human T-cell leukemia virus type-I) infection, in which the closely related target cell-virus-immune system interaction and the time-delay cytotoxic T lymphocyte (CTL) immune response are taken into consideration. Firstly, we give the relevant lemma for the existence of feasible equilibrium points of the model, and then further certify the global asymptotic stabilities of the infection-free equilibrium (IFFE) E1 and the immune-free equilibrium (IMFE) E2. Furthermore, we research the existence of Hopf bifurcation (HB) occurring at the immune equilibrium (IE) E* due to the influence of the delay bifurcation parameter. Also, the numerical simulations confirm this fact. In addition, we obtain the explicit expressions which determine the direction and stability of HB. Finally, a succinct discussion shows that the delay in CTL response can destabilize E* and generate HB, but not affect stabilities of E1 and E2.