A reaction-diffusion model of dengue transmission

Zhiting Xu; Yingying Zhao

doi:10.3934/dcdsb.2014.19.2993

Article Contents

2014, Volume 19, Issue 9: 2993-3018. Doi: 10.3934/dcdsb.2014.19.2993

This issue Previous Article Second moment boundedness of linear stochastic delay differential equations Next Article Global existence and gradient blowup of solutions for a semilinear parabolic equation with exponential source

A reaction-diffusion model of dengue transmission

Zhiting Xu^1, and
Yingying Zhao^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, 2013

Revised: March 31, 2014

Published: October 2014

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Abstract

This paper is devoted to the mathematical analysis of a reaction-diffusion model of dengue transmission. In the case of a bounded spatial habitat, we obtain the local stability as well as the global stability of either disease-free or endemic steady state in terms of the basic reproduction number $\mathcal{R}_0$. In the case of an unbounded spatial habitat, we establish the existence of the traveling wave solutions connecting the two constant steady states when $\mathcal{R}_0>1$, and the nonexistence of the traveling wave solutions that connect the disease-free steady state itself when $\mathcal{R}_0<1$. Numerical simulations are performed to illustrate the main analytic results.

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Mathematics Subject Classification: Primary: 34D20, 35C07; Secondary: 35Q92, 92D30.

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