Travelling wave solutions for delayed lattice reaction-diffusion systems

In this work, we investigate the existence of increasing travelling wave solutions for a class of delayed lattice reaction-diffusion systems. The systems arise from various epidemic and biological models. Instead of using the monotone iteration technique, in this article we first consider a sequence of truncated problems and obtain increasing solutions of the truncated problems. Then, combining solutions of the truncated problems with positive super-solutions of the reaction-diffusion systems and using Helly's convergence lemma, we establish the existence of increasing travelling wave solutions. Moreover, for different non-linearities, we provide some necessary conditions of wave speed for the existence of travelling wave solutions and apply our results to several models.