Impulsive vaccination of SEIR epidemic model with time delay and nonlinear incidence rate

Authors:
Zhong Zhao;Lansun Chen;Xinyu Song
Affiliations:
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China and Department of Mathematics, Huanghuai Normal University, Zhumadian 463000, Henan, PR China;Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China;Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan, PR China
Venue:
Mathematics and Computers in Simulation
Year:
2008

Citing 2
Cited 2

Theoretical examination of the pulse vaccination policy in the SIR epidemic model

Mathematical and Computer Modelling: An International Journal
Hopf bifurcation in epidemic models with a latent period and nonpermanent immunity

Mathematical and Computer Modelling: An International Journal

Dynamic analysis of an ecological model with impulsive control strategy and distributed time delay

Mathematics and Computers in Simulation
Global stability of the endemic equilibrium of multigroup SIR models with nonlinear incidence

Computers & Mathematics with Applications

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Abstract

In this paper, an SEIR epidemic disease model with time delay and nonlinear incidence rate is studied, and the dynamical behavior of the model under pulse vaccination is analyzed. Using the discrete dynamical system determined by the stroboscopic map, we show that there exists an infection-free periodic solution. Further, we show that the infection-free periodic solution is globally attractive when the period of impulsive effect is less than some critical value. Using a new modelling method, we obtain a sufficient condition for the permanence of the epidemic model with pulse vaccination. We show that time delay, pulse vaccination can bring different effects on the dynamic behavior of the model by numerical analysis. Our results also show the time delay is ''profitless''. The main feature of this paper is to introduce time delay and impulse into the SEIR epidemic model and to give pulse vaccination strategies.