Traveling Waves in a Two‐Group Generalized Kermack McKendrick Epidemic Model With Time Delay and Nonlocal Dispersion

Here, we investigate traveling wave existence and nonexistence for a two‐group Kermack McKendrick epidemic model with time delay and nonlocal dispersal. This model is a natural extension of the preceding papers on wave propagation of epidemics (Zhao et al., Nonlinearity 30 (2017) 1287–1325). Our proof establishes the regularity of the traveling wave solutions and constructs suitable sub‐ and super‐solutions using comparison principles under general hypotheses on parameter functions. Furthermore, we show how the introduction of nonlocal dispersal and delay can significantly affect propagation dynamics, altering threshold conditions and deciding at what rate infectious diseases spread or dampen in interconnected populations.