Wave propagations for dispersive variants of spatial models in epidemiology and ecology

Abstract

In this paper, apart from the well-known second-order reaction-diffusion models in epidemiology and ecology, the third-order variants, called the reaction-dispersion models, are proposed. Using an ansatz method with the suitable function, the travelling wave solutions of the corresponding systems are investigated. The long-time behaviour of obtained solutions, which are actually kink type waves, are discussed. It is seen that the proposed system is able to simply display such epidemic model. (C) 2022 Elsevier B.V. All rights reserved.