Threshold dynamics of a bacillary dysentery model withseasonal fluctuation

Zhenguo Bai; Yicang Zhou

doi:10.3934/dcdsb.2011.15.1

Article Contents

2011, Volume 15, Issue 1: 1-14. Doi: 10.3934/dcdsb.2011.15.1

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Threshold dynamics of a bacillary dysentery model with seasonal fluctuation

Zhenguo Bai^1, and
Yicang Zhou^1,

1.
Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049

Received: October 31, 2009

Revised: January 31, 2010

Published: June 2011

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Abstract

A bacillary dysentery model with seasonal fluctuation is formulated and studied. The basic reproductive number $\mathcal {R}_0$ is introduced to investigate the disease dynamics in seasonal fluctuation environments. It is shown that there exists only the disease-free periodic solution which is globally asymptotically stable if $\mathcal {R}_0<1$, and there exists a positive periodic solution if $\mathcal {R}_0>1$. $\mathcal {R}_0$ is a threshold parameter, its magnitude determines the extinction or the persistence of the disease. Parameters in the model are estimated on the basis of bacillary dysentery epidemic data. Numerical simulations have been carried out to describe the transmission process of bacillary dysentery in China.

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Mathematics Subject Classification: Primary: 92D30, 34K13; Secondary: 37N25.

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