Bifurcation analysis in a model of cytotoxic T-lymphocyte response to viral infections

In this paper, we study the dynamics of a mathematical model on primary and secondary cytotoxic T-lymphocyte (CTL) response to viral infections by Wodarz et al. This model has three equilibria and their stability criteria are discussed. The system transitions from one equilibrium to the next as the basic reproductive number, R₀, increases. When R₀ increases even further, we analytically show that periodic solutions may arise from the third equilibrium via Hopf bifurcation. Numerical simulations of the model agree with the theoretical results and these dynamics occur within biologically realistic parameter range. The normal form theory is also applied to find the amplitude, phase and stability information on the limit cycles. Biological implications of the results are discussed.