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Stability analysis of a virus infection model with humoral immunity response and two time delays
Author(s) -
Miao Hui,
Teng Zhidong,
Kang Chengjun,
Muhammadhaji Ahmadjan
Publication year - 2016
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.3790
Subject(s) - mathematics , hopf bifurcation , stability (learning theory) , delay differential equation , bifurcation , lyapunov function , control theory (sociology) , antibody , antibody response , virus , humoral immunity , mathematical analysis , differential equation , immunology , physics , nonlinear system , computer science , biology , control (management) , quantum mechanics , machine learning , artificial intelligence
In this paper, we investigate the dynamical properties for a model of delay differential equations, which describes a virus‐immune interaction in vivo . By analyzing corresponding characteristic equations, the local stability of the equilibria for infection‐free, antibody‐free, and antibody response and the existence of Hopf bifurcation with antibody response delay as a bifurcation parameter at the antibody‐activated infection equilibrium are established, respectively. Global stability of the equilibria for infection‐free, antibody‐free, and antibody response, respectively, also are established by applying the Lyapunov functionals method. The numerical simulations are performed in order to illustrate the dynamical behavior of the model. Copyright © 2016 John Wiley & Sons, Ltd.