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On threshold dynamics for periodic and time-delayed impulsive systems and application to a periodic disease model
Hai-Feng Huo1, Fan Wu1, Hong Xiang1
1Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, China.
Abstract:
The basic reproduction ratio R0 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 R0 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 R0 are obtained. Some numerical simulation results are also given to support our main results.
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