Wang Jinliang, Lang Jiying, Chen Yuming
a School of Mathematical Science , Heilongjiang University , Harbin, People's Republic of China.
b Department of Mathematics , Wilfrid Laurier University , Waterloo , ON , Canada.
J Biol Dyn. 2017 Aug;11(sup2):427-454. doi: 10.1080/17513758.2016.1226436. Epub 2016 Sep 3.
A susceptible-vaccinated-infectious-recovered epidemic model with infection age and relapse age has been formulated. We first address the asymptotic smoothness of the solution semiflow, existence of a global attractor, and uniform persistence of the model. Then by constructing suitable Volterra-type Lyapunov functionals, we establish a global threshold dynamics of the model, which is determined by the basic reproduction number. Biologically, it is confirmed that neglecting the possibility of vaccinees getting infected will over-estimate the effect of vaccination strategies. The obtained results generalize some existing ones.
一个具有感染年龄和复发年龄的易感-接种-感染-康复流行病模型已经建立。我们首先讨论了解半流的渐近光滑性、全局吸引子的存在性以及模型的一致持久性。然后通过构造合适的Volterra型Lyapunov泛函，我们建立了模型的全局阈值动力学，该动力学由基本再生数决定。从生物学角度来看，证实了忽略接种者被感染的可能性会高估疫苗接种策略的效果。所获得的结果推广了一些现有的结果。
