Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rates
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 is permanent by using the Lyapunov functional method. For impulsive vaccination. we obtain two thresholds R* and R* and prove that if R*   I 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. (C) 2009 IMACS. Published by Elsevier B.V. All tights reserved.
impulsive vaccination saturation incidence continuous vaccination permanence global attractivity