Differential Susceptibility SIR Epidemic Model with Time Delay and Pulse Vaccination

Chinese Quarterly Journal of Mathematics ›› 2010, Vol. 25 ›› Issue (2): 228-235.

Differential Susceptibility SIR Epidemic Model with Time Delay and Pulse Vaccination

Department of Mathematics, Huanghuai University

Received:2009-07-19 Online:2010-06-30 Published:2023-06-05
About author: ZHANG Xiu-quan(1974-), male, native of Zhumadian, Henan, a lecturer of Huanghuai University, M.S.D., engages in biomathematics; ZHAO Zhong(1974-), male, native of Zhumadian, Henan, a lecturer of Huanghuai niversity, Ph.D., engages in biomathematics.
Supported by:
Supported by the National Natural Science Foundation of China(10971001)； Supported by Henan Science and Technology Department(082102140025,092300410228)；

Abstract

Abstract: Differential susceptibility SIR epidemic models with time delay and pulse vaccination is studied in this paper. We show that there exists an infection-free periodic solution by using the comparison method, which is globally attractive provided that R₁<1, and that R₂>1 implies the disease is permanent, which means that after some period of time the disease will become endemic.

Key words: impulsive vaccination, periodic solution, global attractivity, permanence

CLC Number:

O175.1

ZHANG Xiu-quan, ZHAO Zhong. Differential Susceptibility SIR Epidemic Model with Time Delay and Pulse Vaccination [J]. Chinese Quarterly Journal of Mathematics, 2010, 25(2): 228-235.

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Differential Susceptibility SIR Epidemic Model with Time Delay and Pulse Vaccination

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