Threshold dynamics of a bacillary dysentery model with
seasonal fluctuation doi:10.3934/dcdsb.2011.15.1
Zhenguo Bai - Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049, China (email) 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.
Keywords: Bacillary dysentery, basic reproductive number, periodic
solution, seasonal fluctuation, global asymptotic stability.
Received: November 2009; Revised: February 2010; Published: October 2010. |
2011 Impact Factor.921
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