Bifurcation analysis of a delayed nonlocal reaction-diffusion system for SARS-CoV-2 infection

Interferons induce an antiviral state in healthy susceptible cells, effectively suppressing the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection. To identify effective interventions during SARS-CoV-2 infection in spatially heterogeneous environments, we develop a novel reaction-diffusion system that incorporates interferon effects, nonlocal infections, and time delay. The basic reproductive ratio (𝓡 0 ) is defined and the threshold dynamics are analyzed. For the spatially homogeneous system, the local Hopf bifurcation at the infection steady state is demonstrated by taking the time delay as the bifurcation parameter, and the global Hopf bifurcation theory is applied to obtain the global extension of periodic solutions. Numerical simulations indicate that: (i)𝓡 0 is a key threshold for viral spread; (ii) the delayed effect of the antiviral responses can induce periodic oscillations of SARS-CoV-2 infection, increasing the difficulty of controlling viral infections; (iii) enhancing the antiviral effects of interferons, initiating interferon responses earlier, and increasing the diffusion rates of productively infected cells and viruses can all effectively control the scale of SARS-CoV-2 infection; and (iv) spatial diffusion and nonlocal infections can effectively regulate and suppress SARS-CoV-2 infection dynamics. This study provides a theoretical basis for understanding SARS-CoV-2 infection mechanisms and designing antiviral strategies.