延迟接种过程与重审队列影响的动态分析

Sudipa Chauhan, Shweta Upadhyaya, Payal Rana, Geetika Malik
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引用次数: 0

摘要

摘要有效的疫苗接种过程需要前所未有的、精确的疫苗接种时间。这项研究基于一种新的数学模型的发展,该模型考虑了由于无法一次性为系统预订时段而导致的疫苗接种延迟。提出了两个模型,其中包括一个延迟微分方程数学模型,并对其进行了动力学分析,以表明疫苗接种的延迟会使系统不稳定。此外,这种延迟导致了排队模型的制定,该模型考虑了以一定速率重试疫苗接种的必要性,因为疫苗接种的延迟可能会产生负面影响。从一个阶段到另一个阶段的转换率遵循指数分布。应用龙格-库塔方法得到了该模型的瞬态概率,并由此得到了性能指标。这些绩效指标包括各州的预期人数。最后,通过数值分析对两种模型进行了验证。我们的结果将特别关注如果延迟时间增加或重审率增加(延迟时间减少)会发生什么。结果表明,第一剂疫苗接种的延迟(即80天)会导致系统不稳定,而两剂疫苗接种同时存在延迟,这会使系统早期不稳定(即第一剂和第二剂分别为80天和120天)。与一剂延迟相比,在两剂疫苗的时段预订延迟的情况下,系统的不稳定速度更快。此外,排队模型的数值结果表明,如果在预订时段的延迟时间内重试率增加,不仅会增加接种疫苗的类别,还会增加康复人群。
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Dynamic analysis of delayed vaccination process along with impact of retrial queues
Abstract An unprecedented and precise time-scheduled rollout for the vaccine is needed for an effective vaccination process. This study is based on the development of a novel mathematical model considering a delay in vaccination due to the inability to book a slot in one go for a system. Two models are proposed which involve a delay differential equation mathematical model whose dynamical analysis is done to show how the delay in vaccination can destabilize the system. Further, this delay led to the formulation of a queuing model that accounts for the need to retry for the vaccination at a certain rate as delay in vaccination can have negative repercussions. The transition rates from one stage to another follow an exponential distribution. The transient state probabilities of the model are acquired by applying the Runge-Kutta method and hence performance indices are also obtained. These performance measures include the expected number of people in various states. Finally, numerical analysis is also provided to validate both models. Our results would specifically focus on what happens if the delay time increases or if the retrial rate increases (delay time decreases). The results reveal that a delay in being vaccinated by the first dose (i.e., 80 days) leads to an unstable system whereas there exists a delay simultaneously in getting vaccinated by both doses that destabilize the system early (i.e., 80 and 120 days for dose one and two, respectively). The system destabilizes faster in the presence of a delay for slot booking for both doses as compared to one dose delay. Further, the numerical results of queuing models show that if the retrial rate increases in this delay time to book the slots, it not only increases in the vaccinated class but also increases the recovered population.
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来源期刊
Computational and Mathematical Biophysics
Computational and Mathematical Biophysics Mathematics-Mathematical Physics
CiteScore
2.50
自引率
0.00%
发文量
8
审稿时长
30 weeks
期刊最新文献
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