Spreading speed and traveling waves for a multi-type SIS epidemic model

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:229

Article

Weng, Peixuan ; Zhao, Xiao-Qiang

关键词: monotone semiflow;    spreading speed;    traveling waves;    SIS epidemic model;   

DOI  :  10.1016/j.jde.2006.01.020

来源: Elsevier

【 摘 要 】

The theory of asymptotic speeds of spread and monotone traveling waves for monotone semiflows is applied to a multi-type SIS epidemic model to obtain the spreading speed c*, and the nonexistence of traveling waves with wave speed c < c*. Then the method of upper and lower solutions is used to establish the existence of monotone traveling waves connecting the disease-free and endemic equilibria for c >= c*. This shows that the spreading speed coincides with the minimum wave speed for monotone traveling waves. We also give an affirmative answer to an open problem presented by Rass and Radcliffe [L. Rass, J. Radcliffe, Spatial Deterministic Epidemics, Math. Surveys Monogr. 102, Amer. Math. Soc., Providence, RI, 2003]. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free