title: Disease control of delay SEIR model with nonlinear incidence rate and vertical transmission.
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 ℜ0 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.
authors.affiliation: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China ; Department of Mathematics, Tonghua Normal University, Tonghua 136000, China.
authors.forename: Yan
authors.initials: Y
authors.lastname: Cheng
authors.affiliation: School of Innovation Experiment, Dalian University of Technology, Dalian 116024, China.
authors.forename: Qiuhui
authors.initials: Q
authors.lastname: Pan
authors.affiliation: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China.
authors.forename: Mingfeng
authors.initials: M
authors.lastname: He
mesh_terms: D000465:Algorithms; D000818:Animals; D050936:Basic Reproduction Number; D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission*; D003198:Computer Simulation; D004196:Disease Outbreaks / Q000517:prevention & control; D004199:Disease Vectors; D058872:Epidemics; D006801:Humans; D015994:Incidence; D018445:Infectious Disease Transmission, Vertical; D008962:Models, Theoretical; D013997:Time Factors; D014611:Vaccination