Traveling wave solutions for a three-component noncooperative systems arising in nonlocal diffusive biological models

Abstract

This paper aims to study the existence of traveling wave solutions (TWS) for a three-component noncooperative systems with nonlocal diffusion. Our main results reveal that when a threshold [Formula: see text], there exists a critical wave speed [Formula: see text]. By using sub- and super-solution methods and Schauder’s fixed point theorem, we prove that the system admits a nontrivial TWS for each [Formula: see text]. Meanwhile, we show that there exists no nontrivial TWS for [Formula: see text] by detailed analysis. Finally, we apply our results to a nonlocal diffusive epidemic model with vaccination, and the boundary asymptotic behavior of TWS for the special case is obtained by constructing a suitable Lyapunov functional. Our research provides some insights on how to deal with the problem of TWS for the nonlocal diffusive epidemic models with bilinear incidence, which extends some results in the previous studies.