1. Dynamics of an HIV infection model with two time delays.
- Author
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Wang, Dianhong, Liu, Yading, Gao, Xiaojie, Wang, Chuncheng, and Fan, Dejun
- Subjects
HIV infections ,HOPF bifurcations ,IMMUNE response ,MATHEMATICAL models - Abstract
In this paper, a mathematical model for HIV-1 infection and immune response is considered, involving two discrete time delays in the intracellular as well as in activation of immune response. Using a recently developed geometric method for studying a class of transcendental equation with two time delays and delay dependent coefficients, we obtain the stability and bifurcation results at the non-trivial equilibrium. In particular, the crossing curves on the two-delays parameter plane can be completely characterized, on which Hopf and double-Hopf bifurcation will take place. In the case of Hopf bifurcation, there exist stability switches, and the direction and stability of delay induced Hopf-bifurcation can be determined using normal form theory and center manifold theorem. These results imply the model will exhibit complex temporal dynamics, such as period oscillations, quasi-periodic solutions, etc. Numerical examples are also carried out to verify these results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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