Threshold dynamics of a bacillary dysentery model withseasonal fluctuation

A bacillary dysentery model with seasonal fluctuation is formulatedand studied. The basic reproductive number R₀ isintroduced to investigate the disease dynamics in seasonalfluctuation environments. It is shown that there exists only thedisease-free periodic solution which is globally asymptoticallystable if R₀1. R₀ is a thresholdparameter, its magnitude determines the extinction or thepersistence of the disease. Parameters in the model are estimated onthe basis of bacillary dysentery epidemic data. Numericalsimulations have been carried out to describe the transmissionprocess of bacillary dysentery in China.