Wang Zhen, Röst Gergely, Moghadas Seyed M
Agent-Based Modelling Laboratory, York University, Toronto, M3J 1P3, Canada.
Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, UK.
J Math Biol. 2019 Dec;79(6-7):2157-2182. doi: 10.1007/s00285-019-01424-6. Epub 2019 Sep 7.
The use of multiple vaccine doses has proven to be essential in providing high levels of protection against a number of vaccine-preventable diseases at the individual level. However, the effectiveness of vaccination at the population level depends on several key factors, including the dose-dependent protection efficacy of vaccine, coverage of primary and booster doses, and in particular, the timing of a booster dose. For vaccines that provide transient protection, the optimal scheduling of a booster dose remains an important component of immunization programs and could significantly affect the long-term disease dynamics. In this study, we developed a vaccination model as a system of delay differential equations to investigate the effect of booster schedule using a control parameter represented by a fixed time-delay. By exploring the stability analysis of the model based on its reproduction number, we show the disease persistence in scenarios where the booster dose is sub-optimally scheduled. The findings indicate that, depending on the protection efficacy of primary vaccine series and the coverage of booster vaccination, the time-delay in a booster schedule can be a determining factor in disease persistence or elimination. We present model results with simulations for a vaccine-preventable bacterial disease, Heamophilus influenzae serotype b, using parameter estimates from the previous literature. Our study highlights the importance of timelines for multiple-dose vaccination in order to enhance the population-wide benefits of herd immunity.
事实证明，使用多剂疫苗对于在个体层面提供针对多种疫苗可预防疾病的高水平保护至关重要。然而，疫苗接种在人群层面的有效性取决于几个关键因素，包括疫苗的剂量依赖性保护效力、初免和加强剂量的覆盖率，尤其是加强剂量的接种时间。对于提供短暂保护的疫苗，加强剂量的最佳接种计划仍然是免疫规划的重要组成部分，并且可能会显著影响疾病的长期动态。在本研究中，我们开发了一个疫苗接种模型，作为一个延迟微分方程组，以使用由固定时间延迟表示的控制参数来研究加强接种计划的效果。通过基于其繁殖数对模型进行稳定性分析，我们展示了在加强剂量接种计划欠佳的情况下疾病的持续存在情况。研究结果表明，根据初免疫苗系列的保护效力和加强疫苗接种的覆盖率，加强接种计划中的时间延迟可能是疾病持续存在或消除的决定性因素。我们使用先前文献中的参数估计值，通过模拟给出了针对一种疫苗可预防细菌性疾病——b型流感嗜血杆菌的模型结果。我们的研究强调了多剂疫苗接种时间安排对于增强群体层面的 herd immunity 益处的重要性。 （注：“herd immunity”直译为“群体免疫”，但在医学领域可能有更专业准确的表述，这里保留英文未翻译，需结合具体专业知识进一步确定准确译法）
