Traveling wave phenomena of a diffusive and vector-bias malariamodel

Zhiting Xu; Yiyi Zhang

doi:10.3934/cpaa.2015.14.923

Article Contents

2015, Volume 14, Issue 3: 923-940. Doi: 10.3934/cpaa.2015.14.923

This issue Previous Article Gradient estimates and comparison principle for some nonlinear elliptic equations Next Article KAM Tori for generalized Benjamin-Ono equation

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

Zhiting Xu^1, and
Yiyi Zhang^2,

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

Received: June 30, 2014

Revised: December 31, 2014

Published: April 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 34C07, 35A10; Secondary: 35Q92, 92D30.

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