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Stability and Hopf bifurcation of a delayed viral infection model with logistic growth and saturated immune impairment
Author(s) -
Jia Jianwen,
Li Jie
Publication year - 2017
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.4648
Subject(s) - hopf bifurcation , center manifold , mathematics , stability (learning theory) , bifurcation , transcritical bifurcation , logistic function , exponential stability , saddle node bifurcation , period doubling bifurcation , bifurcation diagram , mathematical analysis , nonlinear system , physics , statistics , quantum mechanics , machine learning , computer science
In this paper, the stability and Hopf bifurcation of a delayed viral infection model with logistic growth and saturated immune impairment is studied. It is shown that there exist 3 equilibria. The sufficient conditions for local asymptotic stability of the infection‐free equilibrium and no‐immune equilibrium are given. We also discussed the local stability of positive equilibrium and the existence of Hopf bifurcation. Moreover, the direction and stability of Hopf bifurcation is obtained by using standard form theory and the center manifold theorem. Finally, numerical simulations are performed to verify the theoretical conclusions.