# American Institute of Mathematical Sciences

September  2018, 17(5): 1899-1920. doi: 10.3934/cpaa.2018090

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

 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

Received  July 2017 Revised  November 2017 Published  April 2018

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

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.

Citation: Zengji Du, Zhaosheng Feng. Existence and asymptotic behaviors of traveling waves of a modified vector-disease model. Communications on Pure & Applied Analysis, 2018, 17 (5) : 1899-1920. doi: 10.3934/cpaa.2018090
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