Tohoku Mathematical Journal
2002
December
SECOND SERIES VOL. 54, NO. 4

Tohoku Math. J.
54 (2002), 581-591

Title PERMANENCE OF AN SIR EPIDEMIC MODEL WITH DISTRIBUTED TIME DELAYS

Author Wanbiao Ma, Yasuhiro Takeuchi, Tadayuki Hara and Edoardo Beretta

(Received November 24, 2000, revised August 20, 2001)
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.

2000 Mathematics Subject Classification. Primary 92D30; Secondary 92D25, 34K20.

Key words and phrases. Epidemic model, time delay, permanence.

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