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

Cheng Hsiung Hsu, Tzi Sheng Yang

Research output: Contribution to journalArticlepeer-review

61 Scopus citations

Abstract

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.

Original languageEnglish
Article number121
Pages (from-to)121-139
Number of pages19
JournalNonlinearity
Volume26
Issue number1
DOIs
StatePublished - Jan 2013

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