Ziarelli Giovanni, Dede' Luca, Parolini Nicola, Verani Marco, Quarteroni Alfio
MOX, Department of Mathematics, Politecnico di Milano, Milan, Italy.
Institute of Mathematics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland.
Infect Dis Model. 2023 Sep;8(3):672-703. doi: 10.1016/j.idm.2023.05.012. Epub 2023 Jun 5.
In the context of SARS-CoV-2 pandemic, mathematical modelling has played a fundamental role for making forecasts, simulating scenarios and evaluating the impact of preventive political, social and pharmaceutical measures. Optimal control theory represents a useful mathematical tool to plan the vaccination campaign aimed at eradicating the pandemic as fast as possible. The aim of this work is to explore the optimal prioritisation order for planning vaccination campaigns able to achieve specific goals, as the reduction of the amount of infected, deceased and hospitalized in a given time frame, among age classes. For this purpose, we introduce an age stratified -like epidemic compartmental model settled in an abstract framework for modelling two-doses vaccination campaigns and conceived with the description of COVID19 disease. Compared to other recent works, our model incorporates all stages of the COVID-19 disease, including death or recovery, without accounting for additional specific compartments that would increase computational complexity and that are not relevant for our purposes. Moreover, we introduce an optimal control framework where the model is the state problem while the vaccine doses administered are the control variables. An extensive campaign of numerical tests, featured in the Italian scenario and calibrated on available data from Dipartimento di Protezione Civile Italiana, proves that the presented framework can be a valuable tool to support the planning of vaccination campaigns. Indeed, in each considered scenario, our optimization framework guarantees noticeable improvements in terms of reducing deceased, infected or hospitalized individuals with respect to the baseline vaccination policy.
在2019冠状病毒病大流行的背景下,数学建模在进行预测、模拟情景以及评估预防性政治、社会和药物措施的影响方面发挥了重要作用。最优控制理论是一种有用的数学工具,可用于规划旨在尽快根除大流行的疫苗接种活动。这项工作的目的是探索规划疫苗接种活动的最优优先顺序,以实现特定目标,比如在特定时间框架内减少各年龄组的感染、死亡和住院人数。为此,我们引入了一个年龄分层的类似流行病 compartmental 模型,该模型建立在一个抽象框架中,用于对两剂疫苗接种活动进行建模,并结合了对COVID-19疾病的描述。与其他近期工作相比,我们的模型纳入了COVID-19疾病的所有阶段,包括死亡或康复,而无需考虑会增加计算复杂性且与我们的目的无关的额外特定 compartment。此外,我们引入了一个最优控制框架,其中模型是状态问题,而接种的疫苗剂量是控制变量。在意大利情景下进行的广泛数值测试活动,并根据意大利民防部的可用数据进行了校准,证明了所提出的框架可以成为支持疫苗接种活动规划的宝贵工具。事实上,在每个考虑的情景中,我们的优化框架都保证了相对于基线疫苗接种政策,在减少死亡、感染或住院个体方面有显著改善。