Threshold dynamics of a bacillary dysentery model with seasonal fluctuation

Abstract

A bacillary dysentery model with seasonal fluctuation is formu-lated and studied. The basic reproductive number R0 is introduced to inves-tigate the disease dynamics in seasonal fluctuation environments. It is shown that there exists only the disease-free periodic solution which is globally asymp-totically stable if R0 < 1, and there exists a positive periodic solution if R0 > 1. R0 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.