DETERMINISTIC AND STOCHASTIC MODEL FOR HTLV-I INFECTION OF CD4+ T CELLS

摘要

An ODE model of HTLV-I infection with CD4+ T cells is considered and analyzed. The model system has three equilibria: infection free equilibrium, uninfected equilibrium with leukemia cell only and infected equilibrium. It is observed that the infection persists (infected equilibrium is g.a.s.) if basic reproduction number is bigger than one. This model is further modified by introducing discrete time delay to account for the latent period of infection and it is shown that this delay has no destabilizing effect on the local stability of infected equilibrium. Again, this delay model system is extended to corresponding stochastic model considering the randomness in proliferation of leukemia cells. It is done by introducing white noise term in proliferation rate of Leukemia cells and corresponding stochastic delay differential equation model is analyzed using Fourier Transform technique. We observe fluctuations only in Leukemia cells populations and corresponding variations are obtained analytically. A numerical experimentation is performed to analyse and explain the outcomes. We observe that the fluctuations in Leukemia cells' population are contributed by white noise perturbation of proliferation rate and this has no impact of both uninfected and infected CD4+ T cells.