Traveling waves for a lattice dynamical system arising in a diffusive endemic model

TL;DR

This paper investigates traveling wave solutions in a lattice dynamical system modeling disease spread, establishing their existence, minimal wave speed, and non-existence below this speed.

Contribution

It proves the existence of traveling waves, characterizes the minimal wave speed, and shows non-existence of slower waves in a lattice epidemic model.

Findings

Existence of traveling waves connecting disease-free and endemic states

Determination of the minimal wave speed for these waves

Proof of non-existence of waves with speeds below the minimum

Abstract

This paper is concerned with a lattice dynamical system modeling the evolution of susceptible and infective individuals at discrete niches. We prove the existence of traveling waves connecting the disease-free state to non-trivial leftover concentrations. We also characterize the minimal speed of traveling waves and we prove the non-existence of waves with smaller speeds.