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Stability and Hopf bifurcation analysis of immune response delayed HIV type 1 infection model with two target cells
Author(s) -
Balasubramaniam P.,
Prakash M.,
Tamilalagan P.
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3306
Subject(s) - hopf bifurcation , mathematics , jacobian matrix and determinant , stability (learning theory) , bifurcation , control theory (sociology) , immune system , exponential stability , bifurcation diagram , mathematical analysis , type (biology) , nonlinear system , immunology , physics , computer science , medicine , biology , ecology , control (management) , quantum mechanics , machine learning , artificial intelligence
This manuscript presents the HIV‐1 infection model along with cause of differentiation of cytotoxic T lymphocyte response, the total carrying capacity of CD4C + T‐cells, logistic growth term, effect of combination of antiretroviral therapy and discrete type immune response delay. The possibility of existence of multiple equilibriums for the proposed model is analyzed. Asymptotic stability of the non‐delayed infection model is proved from the roots of characteristic equation which are obtained by employing the Jacobian matrix method. The existence of Hopf bifurcation due to immune activation delay is proved. The stability switching is studied by choosing immune activation delay as a bifurcation parameter. Utilizing normal formtheory and centermanifold , we derive the explicit formulae for determining the stability and direction of the periodic solutions bifurcating from Hopf bifurcations. Numerical simulations are executed to verify the derived analytical results. Copyright © 2014 John Wiley & Sons, Ltd.