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Paper   IPM / M / 15172
School of Mathematics
  Title:   Graphical Hopf bifurcation of a Filippov HTLV-1 model with delay in CTLS response
  Author(s):  Elham Shamsara (Joint with Z. Afsharnezhad and E. Javadimanesh)
  Status:   To Appear
  Journal: J. Dynam. Sys.
  Supported by:  IPM
In this paper we present a discontinuous CTLs (Cytotoxic T Lymphocytes) response for HTLV-1. Moreover, a delay parameter for the activation of CTLs is considered. In fact, a system of differential equation with discontinuous right hand side with delay is defined for HTLV-1. For analyzing the dynamical behavior of the system, Graphical Hopf bifurcation is used. In general, Hopf bifurcation theory will help to obtain the periodic solutions of a system as parameter varies. Therefore, by applying the frequency domain approach and analyzing the associated characteristic equation, the existence of Hopf bifurcation, by using delay immune response as a bifurcation parameter is determined. The stability of Hopf bifurcation periodic solutions is obtained by the Nyquist criterion and the Graphical Hopf bifurcation theorem. At the end, numerical simulations is demonstrated our results for the system of HTLV-1.

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