Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rates

Authors:
Juan Hou;Zhidong Teng
Affiliations:
College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, PR China and Department of Applied Mathematics, Xinjiang University of Finance and Economics, Urumqi, 830012, PR Ch ...;College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, PR China
Venue:
Mathematics and Computers in Simulation
Year:
2009

Citing 3
Cited 3

The effect of constant and pulse vaccination on SIR epidemic model with horizontal and vertical transmission

Mathematical and Computer Modelling: An International Journal
Hopf bifurcation in two SIRS density dependent epidemic models

Mathematical and Computer Modelling: An International Journal
Theoretical examination of the pulse vaccination policy in the SIR epidemic model

Mathematical and Computer Modelling: An International Journal

Original article: Global dynamics of an SEIS epidemiological model with time delay describing a latent period

Mathematics and Computers in Simulation
Complex dynamic behavior of three-species ecological model with impulse perturbations and seasonal disturbances

Mathematics and Computers in Simulation
Bifurcation Behaviors Analysis on a Predator---Prey Model with Nonlinear Diffusion and Delay

Journal of Dynamical and Control Systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, two delayed SEIR epidemic models with continuous and impulsive vaccination and saturating incidence are investigated. The dynamical behaviors of the disease are analyzed. For continuous vaccination, we obtain a basic reproductive number R"1 and prove that if R"1@?1 then the disease-free equilibrium is globally attractive and if R"11 then the disease is permanent by using the Lyapunov functional method. For impulsive vaccination, we obtain two thresholds R^* and R"* and prove that if R^*1 then the disease is permanent by using the comparison theorem of impulsive differential equation and the Lyapunov functional method. Lastly, we compared the effects of two vaccination strategies.