# American Institute of Mathematical Sciences

January  2011, 15(1): 1-14. doi: 10.3934/dcdsb.2011.15.1

## Threshold dynamics of a bacillary dysentery model with seasonal fluctuation

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

Received  November 2009 Revised  February 2010 Published  October 2010

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.
Citation: Zhenguo Bai, Yicang Zhou. Threshold dynamics of a bacillary dysentery model with seasonal fluctuation. Discrete & Continuous Dynamical Systems - B, 2011, 15 (1) : 1-14. doi: 10.3934/dcdsb.2011.15.1
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