Traveling Waves in a Lattice Endemic Model With Standard Incidence and Heterogeneous Demographic Dynamics

ABSTRACT This paper investigates traveling wave solutions (TWS) of a lattice dynamical endemic model, which adopts standard incidence, heterogeneous diffusion, and separate demographic parameters for susceptible and infected populations to capture more realistic epidemiological features. By constructing appropriate upper and lower solutions combined with Schauder's fixed point theorem, we rigorously establish the existence of positive, bounded, nontrivial TWS connecting the disease‐free equilibrium to the endemic equilibrium for all supercritical and critical wave speeds. Furthermore, using contradiction arguments and bilateral Laplace transforms, we prove the nonexistence of TWS for subcritical speeds, confirming that the critical speed is exactly the minimal wave speed. Distinct asymptotic decay behaviors of the infected component at critical and supercritical speeds are explicitly characterized. Numerical simulations are performed to verify the theoretical results and illustrate the effects of key parameters on wave propagation.