In this paper, we propose a delayed viral infection model with mitosis of uninfected target cells, two infection modes (virus-to-cell transmission and cell-to-cell transmission), and immune response. The model involves intracellular delays during the processes of viral infection, viral production, and CTLs recruitment. We verify that the threshold dynamics are determined by the basic reproduction number $ R_0 $ for infection and the basic reproduction number $ R_{IM} $ for immune response. The model dynamics become very rich when $ R_{IM} > 1 $. In this case, we use the CTLs recruitment delay $ \tau_3 $ as the bifurcation parameter to obtain stability switches on the positive equilibrium and global Hopf bifurcation diagrams for the model system. This allows us to show that $ \tau_3 $ can lead to multiple stability switches, the coexistence of multiple stable periodic solutions, and even chaos. A brief simulation of two-parameter bifurcation analysis indicates that both the CTLs recruitment delay $ \tau_3 $ and the mitosis rate $ r $ have a strong impact on the viral dynamics, but they do behave differently.
Citation: Jiawei Deng, Ping Jiang, Hongying Shu. Viral infection dynamics with mitosis, intracellular delays and immune response[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 2937-2963. doi: 10.3934/mbe.2023139
In this paper, we propose a delayed viral infection model with mitosis of uninfected target cells, two infection modes (virus-to-cell transmission and cell-to-cell transmission), and immune response. The model involves intracellular delays during the processes of viral infection, viral production, and CTLs recruitment. We verify that the threshold dynamics are determined by the basic reproduction number $ R_0 $ for infection and the basic reproduction number $ R_{IM} $ for immune response. The model dynamics become very rich when $ R_{IM} > 1 $. In this case, we use the CTLs recruitment delay $ \tau_3 $ as the bifurcation parameter to obtain stability switches on the positive equilibrium and global Hopf bifurcation diagrams for the model system. This allows us to show that $ \tau_3 $ can lead to multiple stability switches, the coexistence of multiple stable periodic solutions, and even chaos. A brief simulation of two-parameter bifurcation analysis indicates that both the CTLs recruitment delay $ \tau_3 $ and the mitosis rate $ r $ have a strong impact on the viral dynamics, but they do behave differently.
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Jiawei Deng, Ping Jiang, Hongying Shu. Viral infection dynamics with mitosis, intracellular delays and immune response[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 2937-2963. doi: 10.3934/mbe.2023139
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