Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 111, Issue -, Pages 66-81Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2014.08.012
Keywords
Traveling wave solutions; Minimal wave speed; Kermack-Mckendrick epidemic model; Saturating incidence rate; Latent period
Categories
Funding
- NSF of China [11171120]
- NSF of Guangdong Province [S2012010010034, S2013010013050]
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This paper is devoted to the study of a Kermack-Mckendrick epidemic model with diffusion and latent period. We first consider the well-posedness of solutions of the model. Furthermore, using the Schauder fixed point theorem and Laplace transform, we show that if the threshold value R-0 > 1, then there exists c* > 0 such that for every c > c*, the model admits a traveling wave solution, and if R-0 < 1 and c >= 0; or R-0 > 1 and c is an element of(0, c*), then the model admits no traveling wave solutions. Hence, the existence and nonexistence of traveling wave solutions is determined completely by R-0, and the constant c* is the minimum speed for the existence of traveling wave solutions of the model. (C) 2014 Elsevier Ltd. All rights reserved.
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