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

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. • The third-order variants of models in Biology are studied. • Proposed systems are called as the reaction–dispersion systems. • Dispersion effect in epidemiology and ecology are discussed. • One of the efficient symbolic computation, called the tanh method, is used. • Kink-type waves are obtained. [ABSTRACT FROM AUTHOR]