SVEIR EPIDEMIOLOGICAL MODEL WITH VARYING INFECTIVITY AND DISTRIBUTED DELAYS
SVEIR EPIDEMIOLOGICAL MODEL WITH VARYING INFECTIVITY AND DISTRIBUTED DELAYS
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具有不同传染性和分布式延迟的 Sveir 流行病学模型
DOI：
10.3934/mbe.2011.8.875
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发表时间：
2011-07-01
影响因子：
2.6
通讯作者：
Liu, Shengqiang
中科院分区：
文献类型：
--
作者：
Wang, Jinliang;Huang, Gang;Liu, Shengqiang
在本文中，基于SEIR流行病模型的分布时滞，以考虑不同的传染性，我们引入了疫苗接种室，导致SVEIR模型。利用直接李雅普诺夫方法和LaSalle不变性原理，我们构造了适当的泛函对过去的状态进行积分，建立了全局渐近稳定的条件，这些条件完全由基本再生数R（0）（V）决定.更确切地说，它表明，如果R（0）（V）1，则存在唯一的地方病平衡点是全局渐近稳定的。数学结果表明，接种疫苗是通过减少基本繁殖数有助于疾病控制。然而，成功消除疾病有一个必要条件。如果可以忽略疫苗接种者获得免疫力的时间或在获得免疫力之前被感染的可能性，则满足了这一条件，并且总是可以通过一些合适的疫苗接种策略来根除疾病。这可能会导致过度评估疫苗接种的效果。
In this paper, based on an SEIR epidemiological model with distributed delays to account for varying infectivity, we introduce a vaccination compartment, leading to an SVEIR model. By employing direct Lyapunov method and LaSalle's invariance principle, we construct appropriate functionals that integrate over past states to establish global asymptotic stability conditions, which are completely determined by the basic reproduction number R(0)(V). More precisely, it is shown that, if R(0)(V) 1, then there exists a unique endemic equilibrium which is globally asymptotically stable. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccinees to obtain immunity or the possibility for them to be infected before acquiring immunity can be neglected, this condition would be satisfied and the disease can always be eradicated by some suitable vaccination strategies. This may lead to over-evaluating the effect of vaccination.