Existence and asymptotic behaviors of traveling waves of a modified vector-disease model

Zengji Du; Zhaosheng Feng

doi:10.3934/cpaa.2018090

Article Contents

2018, Volume 17, Issue 5: 1899-1920. Doi: 10.3934/cpaa.2018090

This issue Previous Article Blow-up solutions for a Kirchhoff type elliptic equation with trapping potential Next Article Global synchronising behavior of evolution equations with exponentially growing nonautonomous forcing

Existence and asymptotic behaviors of traveling waves of a modified vector-disease model

Zengji Du^1, and
Zhaosheng Feng^2, ,

1.
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China
2.
School of Mathematical and Statistical Sciences, University of Texas-Rio Grande Valley, Edinburg, Texas 78539, USA

* Corresponding author
* Corresponding author

Received: July 2017

Revised: November 2017

Published: April 2018

This work is supported by NSF of China (Grants No. 11471146,11771185 and 11671176).

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Abstract

In this paper, we are concerned with the existence and asymptotic behavior of traveling wave fronts in a modified vector-disease model. We establish the existence of traveling wave solutions for the modified vector-disease model without delay, then explore the existence of traveling fronts for the model with a special local delay convolution kernel by employing the geometric singular perturbation theory and the linear chain trick. Finally, we deal with the local stability of the steady states, the existence and asymptotic behaviors of traveling wave solutions for the model with the convolution kernel of a special non-local delay.

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Mathematics Subject Classification: Primary: 35Q92, 92D25; Secondary: 35B40, 34D15.

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