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

Jinling Zhou; Yu Yang

doi:10.3934/dcdsb.2017082

Article Contents

2017, Volume 22, Issue 4: 1719-1741. Doi: 10.3934/dcdsb.2017082

This issue Previous Article Random attractor for stochastic Boissonade system with time-dependent deterministic forces and white noises Next Article Instantaneous shrinking and extinction for a non-Newtonian polytropic filtration equation with orientated convection

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

Jinling Zhou and
Yu Yang^,

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

Author Bio: E-mail address: jlzhou@amss.ac.cn; E-mail address: yangyyj@126.com
* Corresponding author: yangyyj@126.com
* Corresponding author: yangyyj@126.com

Received: December 2015

Revised: November 2016

Published: August 2017

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

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Abstract

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.

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Mathematics Subject Classification: Primary:92D30, 35K57;Secondary:34B40.

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