Viral dynamics of an HTLV-I infection model with intracellular delay and CTL immune response delay

Abstract

We have developed a model of HTLV-I infection with two time delays: an intracellular delay, and a CTL immune response delay. The basic reproduction number R0, which depends on the intracellular delay, is shown to determine stability conditions of the model steady states. If R0<1, using a suitable Lyapunov function, we show that the infection-free steady state is globally asymptotically stable including both time delays. If R0>1, the unique infected steady state exists, and we analyze our model in two cases: (a) the model only with the intracellular delay, that has an infected steady state that is globally asymptotically stable for every intracellular delay (shown using suitable Lyapunov functions); (b) the model with the immune response delay only, that experiences a destabilization of the infected steady state leading to Hopf bifurcation and periodic solutions. Furthermore, we employ Latin hypercube sampling (LHS) to investigate the possibility of the occurrence of the Hopf bifurcation and determine the key parameters that affect the stability of the infected steady state, under realistic parameter space. Numerical simulations indicate that an increase of the intracellular delay can cause the infected steady state to stabilize, while an increase of the immune delay can cause it to destabilize.