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

Hai-Feng Huo; Fan Wu; Hong Xiang; Hai-Feng Huo; Fan Wu; Hong Xiang

doi:10.3934/mbe.2022038

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 1: 836-854. doi: 10.3934/mbe.2022038

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

Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, China

Received: 19 September 2021 Accepted: 11 November 2021 Published: 22 November 2021

The basic reproduction ratio $ \mathcal{R}_{0} $ 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 $ \mathcal{R}_{0} $ 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 $ \mathcal{R}_{0} $ are obtained. Some numerical simulation results are also given to support our main results.
- impulsive models,
- time delay,
- basic reproduction ratio,
- swine parasitic disease,
- threshold dynamics
Citation: Hai-Feng Huo, Fan Wu, Hong Xiang. On threshold dynamics for periodic and time-delayed impulsive systems and application to a periodic disease model[J]. Mathematical Biosciences and Engineering, 2022, 19(1): 836-854. doi: 10.3934/mbe.2022038

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Abstract

The basic reproduction ratio $ \mathcal{R}_{0} $ 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 $ \mathcal{R}_{0} $ 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 $ \mathcal{R}_{0} $ are obtained. Some numerical simulation results are also given to support our main results.

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