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1. Threshold dynamics of an HIV-1 model with both virus-to-cell and cell-to-cell transmissions, immune responses, and three delays.

Author

Miao, Hui and Jiao, Meiyan

Subjects
IMMUNE response, HUMORAL immunity, HIV, CYTOTOXIC T cells, HOPF bifurcations, BIFURCATION theory, HOPFIELD networks, T cells
Abstract

In this paper, the dynamical behaviors of a multiple delayed HIV-1 infection model which describes the interactions of humoral, cytotoxic T lymphocyte (CTL) immune responses, and two modes of transmission that are the classical virus-to-cell infection and the direct cell-to-cell transmission are investigated. The model incorporates three delays, including the delays of cell infection, virus production and activation of immune response. We first prove the well-posedness of the model, and calculate the biological existence of equilibria and the reproduction numbers, which contain virus infection, humoral immune response, CTL immune response, CTL immune competition, and humoral immune competition. Further, the threshold conditions for the local and global stability of the equilibria for infection-free, immune-free, antibody response, CTL response, and interior are established by utilizing linearization method and the Lyapunov functionals. The existence of Hopf bifurcation with immune delay as a bifurcation parameter is investigated by using the bifurcation theory. Numerical simulations are carried out to illustrate the theoretical results and reveal the effects of some key parameters on viral dynamics. [ABSTRACT FROM AUTHOR]

Published
2023
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2. Hopf bifurcation and chaos of tumor-Lymphatic model with two time delays.

Author

Wang, Jingnan, Shi, Hongbin, Xu, Li, and Zang, Lu

Subjects
*HOPF bifurcations, *T cells, *BIFURCATION theory, *LYMPHATICS, *CELL proliferation, *IMMUNE system
Abstract

• Obtain threshold values and formulas of the Hopf bifurcation. • Show the interesting chaotic attractors and the periodic oscillation. • Use bifurcation theory to explain the chaotic attractor formation. • Obtain the biomedical significance corresponding to model dynamics. In this paper, a tumor and Lymphatic immune system interaction model with two time delays is discussed in which the delays describe the proliferation of tumor cells and the transmission from immature T lymphocytes to mature T lymphocytes respectively. Conditions for the asymptotic stability of the equilibrium and the existence of Hopf bifurcations are obtained by analyzing the roots of a characteristic equation. The computing formulas for the stability and the direction of the Hopf bifurcating periodic solutions are given. Numerical simulation show that different values of time delays can generate different behaviors, including the stable-state, the periodic oscillation and the chaotic attractors, as well as the coexistence of two periodic oscillations. These theoretical and numerical results not only can be useful for explaining the occurrence of chaotic attractors, but also can help for understanding the biomedical significance corresponding to the interaction dynamics of tumor cells and T lymphocytes. [ABSTRACT FROM AUTHOR]

Published
2022
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