Disease Control of Delay SEIR Model with Nonlinear Incidence Rate and Vertical Transmission. (12th December 2013)

• Record Type: Journal Article
• Authors: Cheng, Yan; Pan, Qiuhui; He, Mingfeng
• Other Names: Imoto Seiya Academic Editor.
• Is Part Of: Computational and mathematical methods in medicine. Volume 2013(2013)
• Publication Date: 2013-12-12
• Subjects: Medicine -- Computer simulation -- Periodicals; Medicine -- Mathematical models -- Periodicals; 610.11
• DOI: 10.1155/2013/830237
• Languages: English
• ISSNs: 1748-670X

Abstract

Abstract : The aim of this paper is to develop two delayed SEIR epidemic models with nonlinear incidence rate, continuous treatment, and impulsive vaccination for a class of epidemic with latent period and vertical transition. For continuous treatment, we obtain a basic reproductive number ℜ 0 and prove the global stability by using the Lyapunov functional method. We obtain two thresholds ℜ * and ℜ * for impulsive vaccination and prove that if ℜ * < 1, then the disease-free periodic solution is globally attractive and if ℜ * > 1, then the disease is permanent by using the comparison theorem of impulsive differential equation. Numerical simulations indicate that pulse vaccination strategy or a longer latent period will make the population size infected by a disease decrease.