# American Institute of Mathematical Sciences

May  2015, 14(3): 923-940. doi: 10.3934/cpaa.2015.14.923

## Traveling wave phenomena of a diffusive and vector-bias malaria model

 1 School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong 510631 2 School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

Received  July 2014 Revised  January 2015 Published  March 2015

This paper is devoted to the study of a diffusive and vector-bias malaria model. We first analyze the well-posedness of the initial value problem of the model. Then, according to the basic reproduction ratio $\mathcal{R}_0$, we establish the existence and non-existence of traveling wave solutions for the model. The proof of the main theorems is based on Schauder fixed point theorem and the variation of constants formula of ODEs.
Citation: Zhiting Xu, Yiyi Zhang. Traveling wave phenomena of a diffusive and vector-bias malaria model. Communications on Pure & Applied Analysis, 2015, 14 (3) : 923-940. doi: 10.3934/cpaa.2015.14.923
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