Bifurcation analysis of the Nowak–Bangham model in CTL dynamics

Abstract

This paper investigates the local bifurcations of a CTL response model published by Nowak and Bangham [M.A. Nowak, C.R.M. Bangham, Population dynamics of immune responses to persistent viruses, Science 272 (1996) 74]. The Nowak–Bangham model can have three equilibria depending on the basic reproduction number, and generates a Hopf bifurcation through two bifurcations of equilibria. The main result shows a sufficient condition for the interior equilibrium to have a unique bifurcation point at which a simple Hopf bifurcation occurs. For this proof, some new techniques are developed in order to apply the method established by Liu [W.M. Liu, Criterion of Hopf bifurcations without using eigenvalues, J. Math. Anal. Appl. 182 (1) (1994) 250]. In addition, to demonstrate the result obtained theoretically, some bifurcation diagrams are presented with numerical examples.