Existence and critical speed of traveling wave fronts in a modified vector disease model with distributed delay

Abstract

In this paper, we consider a modified disease model with distributed delay. The existence of traveling wave fronts connecting the zero equilibrium and the positive equilibrium is established by using an iterative technique and a nonstandard ordering for the set of profiles of the corresponding wave system. We also study the critical wave speed and give a detailed analysis on its location and asymptotic behavior with respect to the time delay. Our work extends some previous results.

Traveling wave solutions in n-dimensional delayed nonlocal diffusion system with mixed quasimonotonicity

“…[16,18,6,2,1,5,10,21,24]). Schaaf [15] systematically studied two scalar reactiondiffusion equations with a single discrete delay for the so-called Huxley nonlinearity as well as Fisher nonlinearity by using the phase space analysis, the maximum principle for parabolic functional differential equations and the general theory for ordinary functional differential equations.…”

Existence and Asymptotic Behavior of Traveling Wave Fronts for a Time-Delayed Degenerate Diffusion Equation

“…which describes the propagation of a voltage pulse through the nerve axon of a squid. Recently, more and more attention has been paid to the linear and semilinear parabolic equations with and without time delay; see, for example, [2][3][4][5][6][7]. A natural extension of the H-H model is the following linear diffusion equation:…”