Filomat, ( ISI ), Year (2017-3)

Title : ( Hopf bifurcation for a discontinuous HTLV-1 model )

Authors: Elham Shamsara , Zahra Afsharnejad , REIHANEH MOSTOLIZADEH ,

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Developing accurate mathematical models for host immune response in immunosuppressive diseases such as HIV and HTLV-1 are essential to achieve an optimal drug therapy regime. Since for HTLV-1 specific CTL response typically occurs after a time lag, we consider a discontinuous response function to better describe this lagged response during the early stage of the infectious, thus the system of HTLV-1 model will be a discontinuous system. For analyzing the dynamic of the system we use Filippov theory and find conditions in which the Filippov system undergoes a Hopf bifurcation. The Hopf bifurcation help us to find stable and unstable periodic oscillations and can be used to predict whether the CTL response can return to a steady state condition. Also, Hopf bifurcation in sliding mode is investigated. In this case the solutions will remain in the hyper-surface of discontinuity and as a consequence the disease cannot progress, at least for a long time. Finally we use numerical simulations to demonstrate the results by example.


, CTL response, discontinuous system, HAM/TSP, Hopf bifurcation, HTLV-1 infection
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author = {Shamsara, Elham and Afsharnejad, Zahra and MOSTOLIZADEH, REIHANEH},
title = {Hopf bifurcation for a discontinuous HTLV-1 model},
journal = {Filomat},
year = {2017},
month = {March},
issn = {0354-5180},
keywords = {CTL response; discontinuous system; HAM/TSP; Hopf bifurcation; HTLV-1 infection},


%0 Journal Article
%T Hopf bifurcation for a discontinuous HTLV-1 model
%A Shamsara, Elham
%A Afsharnejad, Zahra
%J Filomat
%@ 0354-5180
%D 2017