On threshold dynamics for periodic and time-delayed impulsive systems and application to a periodic disease model.

The basic reproduction ratio R of more general periodic and time-delayed impulsive model which the period of model coefficients is different from that of fixed impulsive moments, is developed. That R is the threshold parameter for the stability of the zero solution of the associated linear system is also shown. The developed theory is further applied to a swine parasitic disease model with pulse therapy. Threshold results on its global dynamics in terms of R are obtained. Some numerical simulation results are also given to support our main results.