Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2013-07-01

Journal: COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE

Included Journals: Scopus、PubMed、SCIE

Volume: 2013

Page Number: 830237

ISSN: 1748-670X

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.