# American Institute of Mathematical Sciences

May  2015, 14(3): 1001-1022. doi: 10.3934/cpaa.2015.14.1001

## 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, China

Received  September 2014 Revised  January 2015 Published  March 2015

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.
Citation: Yan Li, Wan-Tong Li, Guo Lin. Traveling waves of a delayed diffusive SIR epidemic model. Communications on Pure & Applied Analysis, 2015, 14 (3) : 1001-1022. doi: 10.3934/cpaa.2015.14.1001
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