Threshold dynamics of a bacillary dysentery model withseasonal fluctuation
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.
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