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Modeling Inhibitory Effect on the Growth of Uninfected T Cells Caused by Infected T Cells: Stability and Hopf
Yahui Ji1, Wanbiao Ma1, Keying Song1
1Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, 100083, Beijing, China.
Abstract:
We consider a class of viral infection dynamic models with inhibitory effect on the growth of uninfected T cells caused by infected T cells and logistic target cell growth. The basic reproduction number R 0 is derived. It is shown that the uninfected equilibrium is globally asymptotically stable if R 0 < 1. Sufficient conditions for the existence of Hopf bifurcation at the infected equilibrium are investigated by analyzing the distribution of eigenvalues. Furthermore, the properties of Hopf bifurcation are determined by the normal form theory and the center manifold. Numerical simulations are carried out to support the theoretical analysis.
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