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Article

Impulsive Linearly Implicit Euler Method for the SIR Epidemic Model with Pulse Vaccination Strategy

by
Gui-Lai Zhang
*,
Zhi-Yong Zhu
,
Lei-Ke Chen
and
Song-Shu Liu
College of Sciences, Northeastern University, Shenyang 110819, China
*
Author to whom correspondence should be addressed.
Axioms 2024, 13(12), 854; https://doi.org/10.3390/axioms13120854
Submission received: 7 November 2024 / Revised: 2 December 2024 / Accepted: 3 December 2024 / Published: 4 December 2024
(This article belongs to the Special Issue Differential Equations and Inverse Problems, 2nd Edition)
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Abstract

In this paper, a new numerical scheme, which we call the impulsive linearly implicit Euler method, for the SIR epidemic model with pulse vaccination strategy is constructed based on the linearly implicit Euler method. The sufficient conditions for global attractivity of an infection-free periodic solution of the impulsive linearly implicit Euler method are obtained. We further show that the limit of the disease-free periodic solution of the impulsive linearly implicit Euler method is the disease-free periodic solution of the exact solution when the step size tends to 0. Finally, two numerical experiments are given to confirm the conclusions.
Keywords: impulsive linearly implicit Euler method; global attractivity; disease-free periodic solution impulsive linearly implicit Euler method; global attractivity; disease-free periodic solution

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MDPI and ACS Style

Zhang, G.-L.; Zhu, Z.-Y.; Chen, L.-K.; Liu, S.-S. Impulsive Linearly Implicit Euler Method for the SIR Epidemic Model with Pulse Vaccination Strategy. Axioms 2024, 13, 854. https://doi.org/10.3390/axioms13120854

AMA Style

Zhang G-L, Zhu Z-Y, Chen L-K, Liu S-S. Impulsive Linearly Implicit Euler Method for the SIR Epidemic Model with Pulse Vaccination Strategy. Axioms. 2024; 13(12):854. https://doi.org/10.3390/axioms13120854

Chicago/Turabian Style

Zhang, Gui-Lai, Zhi-Yong Zhu, Lei-Ke Chen, and Song-Shu Liu. 2024. "Impulsive Linearly Implicit Euler Method for the SIR Epidemic Model with Pulse Vaccination Strategy" Axioms 13, no. 12: 854. https://doi.org/10.3390/axioms13120854

APA Style

Zhang, G.-L., Zhu, Z.-Y., Chen, L.-K., & Liu, S.-S. (2024). Impulsive Linearly Implicit Euler Method for the SIR Epidemic Model with Pulse Vaccination Strategy. Axioms, 13(12), 854. https://doi.org/10.3390/axioms13120854

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