PERMANENCE OF AN SIR EPIDEMIC MODEL WITH DISTRIBUTED TIME DELAYS

WANBIAO MA; YASUHIRO TAKEUCHI; TADAYUKI HARA; EDOARDO BERETTA

doi:10.2748/tmj/1113247650

Tohoku Mathematical Journal, Second Series

Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735

PERMANENCE OF AN SIR EPIDEMIC MODEL WITH DISTRIBUTED TIME DELAYS

WANBIAO MA, YASUHIRO TAKEUCHI, TADAYUKI HARA, EDOARDO BERETTA

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Keywords: Epidemic model, time delay, permanence

JOURNAL FREE ACCESS

2002 Volume 54 Issue 4 Pages 581-591

DOI https://doi.org/10.2748/tmj/1113247650

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Abstract

We consider permanence of an SIR epidemic model with distributed time delays. Based on some known techniques on limit sets of differential dynamical systems, we show that, for any time delay, the SIR epidemic model is permanent if and only if an endemic equilibrium exits.

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