Bifurcation analysis of the Nowak-Bangham model in CTL dynamics.
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.
Egami
Chikahiro
C
Department of Digital Engineering, Numazu National College of Technology, Numazu, Shizuoka, Japan. egami@numazu-ct.ac.jp
D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D006801:Humans; D018448:Models, Immunological; D013602:T-Lymphocytes, Cytotoxic / Q000166:cytology* / Q000276:immunology*; D014777:Virus Diseases / Q000188:drug therapy / Q000276:immunology* / Q000821:virology*