Existence, uniqueness, monotonicity and asymptotic behaviour of travelling waves for epidemic models

Cheng Hsiung Hsu, Tzi Sheng Yang

研究成果: 雜誌貢獻期刊論文同行評審

70 引文 斯高帕斯(Scopus)

摘要

The purpose of this work is to investigate the existence, uniqueness, monotonicity and asymptotic behaviour of travelling wave solutions for a general epidemic model arising from the spread of an epidemic by oral-faecal transmission. First, we apply Schauder's fixed point theorem combining with a supersolution and subsolution pair to derive the existence of positive monotone monostable travelling wave solutions. Then, applying the Ikehara's theorem, we determine the exponential rates of travelling wave solutions which converge to two different equilibria as the moving coordinate tends to positive infinity and negative infinity, respectively. Finally, using the sliding method, we prove the uniqueness result provided the travelling wave solutions satisfy some boundedness conditions.

原文???core.languages.en_GB???
文章編號121
頁(從 - 到)121-139
頁數19
期刊Nonlinearity
26
發行號1
DOIs
出版狀態已出版 - 1月 2013

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