Dynamical, Stability, and Bifurcation of a Viral Model With General Cell-to-Cell Incidence Rate and Delayed Saturated CTL Immunity

In this paper, we propose a viral model with cell-to-cell propagation, delayed saturated CTL immunity, and general incidence rate. Two biological threshold parameters, namely, the basic reproductive number R0 and the CTL immune reproductive number R1, are derived. We demonstrate the global stability of the two boundary steady points by applying the Lyapunov approach and LaSalle’s invariance principle. If R0≤1, the virus-clear steady point E0 is globally asymptotically stable for any value of delay; if R1≤1 1, the sufficient conditions for the local stability of the infection steady point with CTL response E⋆ are met. We prove the fact that time delay can change the stability of E⋆ and result in the occurrence of Hopf bifurcation. Hopf bifurcation is a type of instability that can cause the system to transition from a stable equilibrium point to an unstable one. This can lead to the virus becoming more virulent or to the development of new strains of the virus. Finally, we provide an application with numerical simulations to confirm our results.