SVIR epidemic models with vaccination strategies
SVIR epidemic models with vaccination strategies
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具有疫苗接种策略的 SVIR 流行病模型
DOI：
10.1016/j.jtbi.2007.10.014
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发表时间：
2008-07-07
影响因子：
2
通讯作者：
Iwami, Shingo
中科院分区：
文献类型：
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作者：
Liu, Xianning;Takeuchi, Yasuhiro;Iwami, Shingo
接种疫苗对消灭传染病很重要。为了完成疫苗接种过程，通常应该多次接种，并且两次接种之间必须有固定的时间间隔。接种者（已开始接种过程的易感个体）与易感个体和恢复个体不同。考虑到接种者获得免疫力的时间以及在此之前被感染的可能性，建立了两个SVIR模型，分别描述了连续接种策略和脉冲接种策略（PVS）。结果表明，这两个系统都表现出严格的阈值动态依赖于基本再生数。如果这个数字低于1，疾病就可以被根除。如果它大于1，则在正平衡点的全局渐近稳定性和疾病持久性的意义下，该疾病是地方病。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。如果忽略接种者获得免疫力的时间或在此之前被感染的可能性，这种情况就消失了，疾病总是可以通过一些适当的接种策略根除的。这可能会导致过度评估疫苗接种的效果。(c)2007爱思唯尔有限公司保留所有权利。
Vaccination is important for the elimination of infectious diseases. To finish a vaccination process, doses usually should be taken several times and there must be some fixed time intervals between two doses. The vaccinces (susceptible individuals who have started the vaccination process) are different from both susceptible and recovered individuals. Considering the time for them to obtain immunity and the possibility for them to be infected before this, two SVIR models are established to describe continuous vaccination strategy and pulse vaccination strategy (PVS), respectively. It is shown that both systems exhibit strict threshold dynamics which depend on the basic reproduction number. If this number is below unity, the disease can be eradicated. And if it is above unity, the disease is endemic in the sense of global asymptotical stability of a positive equilibrium for continuous vaccination strategy and disease permanence for PVS. 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 this is neglected, this condition disappears and the disease can always be eradicated by some suitable vaccination strategies. This may lead to over-evaluating the effect of vaccination. (c) 2007 Elsevier Ltd. All rights reserved.