Journal of Clinical Medicine Research

There is an inherent time delay in the CD8T cell response itself, and viral spread leads to spatially heterogeneous characteristics of infection. Currently, there is a lack of in-depth research on the combined effect of these two factors. This study constructs a partial functional differential equation model that combines the CTL amplification delay and the viral spread process, which not only demonstrates the forward boundability of the model solution but also clearly defines the basic reproduction number of the virus and immunity. Using the analysis method of characteristic equations, the study obtained the critical conditions for Turing instability in the pure diffusion scenario and the criteria for Hopf branching in the pure delay scenario respectively. In the delay-diffusion two-parameter plane, the study further identified the specific regions of the Turing-Hopf double instability. The numerical simulation results show that the system has multiple behavioral patterns such as uniform steady state, time-period oscillation, and spatiotemporal chaos. This result also reveals that the infection outcome is non-monotonic regulated by the ratio of delay length to diffusion rate. The model framework provides a new approach to understanding the spatiotemporal complexity of CTL antiviral immunity, and also has theoretical implications for optimizing relevant intervention strategies.