# American Institute of Mathematical Sciences

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June  2017, 22(4): 1719-1741. doi: 10.3934/dcdsb.2017082

## Traveling waves for a nonlocal dispersal SIR model with general nonlinear incidence rate and spatio-temporal delay

 School of Science and Technology, Zhejiang International Studies University, Hangzhou 310012, China

* Corresponding author: yangyyj@126.com

Received  December 2015 Revised  November 2016 Published  February 2017

Fund Project: Supported by the National Natural Science Fund of China (Nos. 11501518, 11501519 and 11626219)

In this paper, we study a nonlocal dispersal SIR model with general nonlinear incidence rate and spatio-temporal delay. By Schauder's fixed point theorem and Laplace transform, we show that the existence and nonexistence of traveling wave solutions are determined by the basic reproduction number and the minimal wave speed. Some examples are listed to illustrate the theoretical results. Our results generalize some known results.

Citation: Jinling Zhou, Yu Yang. Traveling waves for a nonlocal dispersal SIR model with general nonlinear incidence rate and spatio-temporal delay. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1719-1741. doi: 10.3934/dcdsb.2017082
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