Delay induced travelling wavefronts in a diffusive vector disease model with distributed delay

Abstract

The existence of travelling wavefront solutions is established for a reaction diffusion equation with distributed delay, which models vector disease. Instead of geometric perturbation method, the approach used here is the upper---lower solution technique and monotone iteration recently developed by Wang et al. [J. Differ. Equations 222 (2006), pp. 185---232)] and the result shows that delay can indeed induce slow travelling wavefronts.