Amira Bouhali, Walid Ben Aribi, Slimane Ben Miled, Amira Kebir
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引用次数: 0
摘要
针对 COVID-19 制定有效的疫苗接种策略仍然是全球公共卫生领域的一项重要工作,尤其是在免疫力下降和流行病学动态不断变化所带来的挑战下。本研究通过考虑年龄结构、免疫动态和不同的最大接种率,研究了最佳疫苗接种策略。为此,我们建立了一个分层为 $ n $ 年龄段的 SEIR 模型,将疫苗接种率作为最优控制问题中与年龄相关的控制变量。我们制定了一个目标函数,旨在最大限度地降低临界感染率,同时优化疫苗接种工作,然后进行了严格的数学分析,以确保最优控制的存在和特征。利用三个国家不同年龄分布的数据,在扩张型、收缩型和静止型金字塔中,我们进行了数值模拟,以评估与年龄相关的最佳疫苗接种策略、临界感染数和疫苗接种频率。我们的研究结果凸显了最大接种率对形成最佳接种策略的重要影响。在最大接种率恒定的情况下,根据人口统计学确定年龄组的优先次序证明是有效的,接种率越高,所有年龄分布的危重感染者人数越少。相反,采用与年龄相关的最大疫苗接种率(类似于世卫组织的策略)可能并不总能带来最低的临界感染峰值,但在资源有限的情况下却是一种可行的选择。
Impact of immunity loss on the optimal vaccination strategy for an age-structured epidemiological model.
The pursuit of effective vaccination strategies against COVID-19 remains a critical endeavour in global public health, particularly amidst challenges posed by immunity loss and evolving epidemiological dynamics. This study investigated optimal vaccination strategies by considering age structure, immunity dynamics, and varying maximal vaccination rates. To this end, we formulated an SEIR model stratified into $ n $ age classes, with the vaccination rate as an age-dependent control variable in an optimal control problem. We developed an objective function aimed at minimising critical infections while optimising vaccination efforts and then conducted rigorous mathematical analyses to ensure the existence and characterization of the optimal control. Using data from three countries with diverse age distributions, in expansive, constrictive, and stationary pyramids, we performed numerical simulations to evaluate the optimal age-dependent vaccination strategy, number of critical infections, and vaccination frequency. Our findings highlight the significant influence of maximal vaccination rates on shaping optimal vaccination strategies. Under constant maximal vaccination rates, prioritising age groups based on population demographics proves effective, with higher rates resulting in fewer critically infected individuals across all age distributions. Conversely, adopting age-dependent maximal vaccination rates, akin to the WHO strategy, may not always lead to the lowest critical infection peaks but offers a viable alternative in resource-constrained settings.
期刊介绍:
Mathematical Biosciences and Engineering (MBE) is an interdisciplinary Open Access journal promoting cutting-edge research, technology transfer and knowledge translation about complex data and information processing.
MBE publishes Research articles (long and original research); Communications (short and novel research); Expository papers; Technology Transfer and Knowledge Translation reports (description of new technologies and products); Announcements and Industrial Progress and News (announcements and even advertisement, including major conferences).