Propagation dynamics of an influenza transmission model with nonlocal dispersal

This paper investigated the existence and nonexistence of traveling wave solutions for a nonlocal dispersal influenza transmission model with human mobility. We established the existence of nonnegative entire solutions by combining the upper-lower solution method with Schauder's fixed point theorem. Appropriate Lyapunov functionals were constructed to determine the asymptotic behavior of solutions at $+\mathrm{\infty }$. Due to the influence of the nonlocal dispersal operator, the asymptotic behavior at $-\mathrm{\infty }$ for the critical wave speed could not be directly established via the Hartman-Grobman theorem. Through careful analysis of the wave equation, we overcame this difficulty and established the desired asymptotic properties. Finally, we used numerical simulations to verify the existence of the traveling wave solution, and compared the effects of the nonlocal dispersal pattern and the local dispersal pattern on the wave speed.