Open AccessBifurcation analysis of HIV-1 infection model with cell-to-cell transmission and immune response delay
Author(s) -
Jin Xu,
Yicang Zhou
Publication year - 2016
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2015006
Subject(s) - center manifold , hopf bifurcation , stability (learning theory) , chaotic , bifurcation , mathematics , immune system , saddle node bifurcation , control theory (sociology) , transmission (telecommunications) , dynamics (music) , transcritical bifurcation , mathematical analysis , physics , biology , computer science , immunology , quantum mechanics , nonlinear system , telecommunications , control (management) , machine learning , artificial intelligence , acoustics
A within-host viral infection model with both virus-to-cell and cell-to-cell transmissions and time delay in immune response is investigated. Mathematical analysis shows that delay may destabilize the infected steady state and lead to Hopf bifurcation. Moreover, the direction of the Hopf bifurcation and the stability of the periodic solutions are investigated by normal form and center manifold theory. Numerical simulations are done to explore the rich dynamics, including stability switches, Hopf bifurcations, and chaotic oscillations.