Aronna M Soledad, Moschen Lucas Machado
School of Applied Mathematics, FGV, Praia de Botafogo, 190, 22250-900, Rio de Janeiro, Brazil.
Infect Dis Model. 2024 Jul 4;9(4):1198-1222. doi: 10.1016/j.idm.2024.06.007. eCollection 2024 Dec.
This study presents a mathematical model for optimal vaccination strategies in interconnected metropolitan areas, considering commuting patterns. It is a compartmental model with a vaccination rate for each city, acting as a control function. The commuting patterns are incorporated through a weighted adjacency matrix and a parameter that selects day and night periods. The optimal control problem is formulated to minimize a functional cost that balances the number of hospitalizations and vaccines, including restrictions of a weekly availability cap and an application capacity of vaccines per unit of time. The key findings of this work are bounds for the basic reproduction number, particularly in the case of a metropolitan area, and the study of the optimal control problem. Theoretical analysis and numerical simulations provide insights into disease dynamics and the effectiveness of control measures. The research highlights the importance of prioritizing vaccination in the capital to better control the disease spread, as we depicted in our numerical simulations. This model serves as a tool to improve resource allocation in epidemic control across metropolitan regions.
本研究提出了一个考虑通勤模式的、用于相互连接的大都市地区最优疫苗接种策略的数学模型。它是一个 compartmental 模型，每个城市都有一个疫苗接种率，作为控制函数。通勤模式通过加权邻接矩阵和一个选择白天和夜间时段的参数来纳入。最优控制问题的制定是为了最小化一个功能成本，该成本平衡了住院人数和疫苗数量，包括每周可用上限的限制以及每单位时间的疫苗接种能力。这项工作的关键发现是基本再生数的界限，特别是在大都市地区的情况下，以及对最优控制问题的研究。理论分析和数值模拟为疾病动态和控制措施的有效性提供了见解。研究强调了在首都优先进行疫苗接种以更好地控制疾病传播的重要性，正如我们在数值模拟中所描述的那样。该模型作为一种工具，用于改善大都市地区疫情防控中的资源分配。
