Asymptotic boundary and nonexistence of traveling waves in a discrete diffusive epidemic model

Abstract

ABSTRACTIn this paper, we establish the asymptotic boundary of traveling waves (first-component) in a discrete diffusive epidemic model, whose existence is well-known. Meanwhile, we derive the nonexistence of traveling wave solutions with non-positive wave speed. We solve two open problems left in two papers [Fu et al., Nonlinear Convex A. 17 (2016), pp. 1739–1751; Wu, J. Differential Equations 262 (2017), pp. 272–282].