School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China ; Department of Mathematics, Tonghua Normal University, Tonghua 136000, China.
School of Innovation Experiment, Dalian University of Technology, Dalian 116024, China.
Comput Math Methods Med. 2013;2013:830237. doi: 10.1155/2013/830237. Epub 2013 Dec 12.
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.
本文旨在建立具有非线性发生率、连续治疗和脉冲接种的两个时滞 SEIR 传染病模型,用于一类具有潜伏期和垂直传播的传染病。对于连续治疗,我们得到了基本再生数 ℜ0,并通过 Lyapunov 函数方法证明了全局稳定性。对于脉冲接种,我们得到了两个阈值 ℜ* 和 ℜ∗,并通过脉冲微分方程比较定理证明了如果 ℜ* < 1,则无病周期解全局吸引,如果 ℜ∗ > 1,则疾病永久存在。数值模拟表明,脉冲接种策略或更长的潜伏期会使受疾病感染的人口数量减少。