Traveling Viral Waves for a Spatial May–Nowak Model with Hybrid Local and Nonlocal Dispersal

To investigate the spatial dynamics of viruses propagating between host cells, the current paper is devoted to studying the existence and nonexistence of viral waves for a reaction–diffusion and May–Nowak system with hybrid dispersal. Specifically, we define a critical wave speed $c^{*}$ threshold to determine the existence of traveling waves when the viral infection reproduction number $R_0>1$. By employing the upper/lower solutions along with the Schauder's fixed-point theorem, the existence of traveling waves connecting the uninfected and infected states is determined for each wave speed $c\ge c^{*}$. Conversely, nonexistence is demonstrated through the application of the negative one-sided Laplace transform for the case . The nonexistence of traveling waves in the $R_0\le 1$ case is also demonstrated. Finally, some novel coupled numerical algorithms are developed to analyze the traveling viral waves and asymptotic spreading speed of the model on account of the actual hybrid dispersal features, which strongly shows that the introduction of nonlocal dispersal will accelerate viral infection.