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Wave propagation for a class of non-local dispersal non-cooperative systems

Published online by Cambridge University Press:  14 March 2019

Fei-Ying Yang
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu730000, China (wtli@lzu.edu.cn)
Wan-Tong Li
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu730000, China (wtli@lzu.edu.cn)
Jia-Bing Wang
Affiliation:
School of Mathematics and Physics, China University of Geosciences (Wuhan), Wuhan430074, China

Abstract

This paper is concerned with the travelling waves for a class of non-local dispersal non-cooperative system, which can model the prey-predator and disease-transmission mechanism. By the Schauder's fixed-point theorem, we first establish the existence of travelling waves connecting the semi-trivial equilibrium to non-trivial leftover concentrations, whose bounds are deduced from a precise analysis. Further, we characterize the minimal wave speed of travelling waves and obtain the non-existence of travelling waves with slow speed. Finally, we apply the general results to an epidemic model with bilinear incidence for its propagation dynamics.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2019

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