Traveling waves of a delayed diffusive SIR epidemic model

Yan Li; Wan-Tong Li; Guo Lin

doi:10.3934/cpaa.2015.14.1001

Article Contents

2015, Volume 14, Issue 3: 1001-1022. Doi: 10.3934/cpaa.2015.14.1001

This issue Previous Article Global existence and optimal decay rates of solutions to a reduced gravity two and a half layer model Next Article Existence results for compressible radiation hydrodynamic equations with vacuum

Traveling waves of a delayed diffusive SIR epidemic model

1.
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000
2.
School of Mathematics and Statistics, Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000

Received: August 31, 2014

Revised: December 31, 2014

Published: April 2015

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Abstract

This paper is concerned with the minimal wave speed of a delayed diffusive SIR epidemic model with Holling-II incidence rate and constant external supplies. By presenting the existence and nonexistence of traveling wave solutions for any positive wave speed, the minimal wave speed is established. In particular, the minimal wave speed decreases when the latency of infection increases. Biologically speaking, the longer the latency of infection in a vector is, the slower the disease spreads.

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Mathematics Subject Classification: Primary: 35K57, 35R20; Secondary: 92D25.

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