Jorge D C P, Oliveira J F, Miranda J G V, Andrade R F S, Pinho S T R
Instituto de Física Teórica, Universidade Estadual Paulista-UNESP, R. Dr. Teobaldo Ferraz 271, São Paulo 01140-070, Brazil.
Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil.
R Soc Open Sci. 2022 Sep 7;9(9):220005. doi: 10.1098/rsos.220005. eCollection 2022 Sep.
The effective reproduction number, , plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual in an epidemic process. Estimation methods for the time evolution of , using incidence data, rely on the generation interval distribution, (), which is usually obtained from empirical data or theoretical studies using simple epidemic models. However, for systems that present heterogeneity, either on the host population or in the expression of the disease, there is a lack of data and of a suitable general methodology to obtain (). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining explicit expressions of the reproduction numbers and the generation interval distributions, within and between model sub-compartments provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of COVID-19 in municipalities of the state of Rio de Janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others.
有效繁殖数(R_t)在传染病研究中起着关键作用，它表示在疫情传播过程中，一个感染个体当前平均引起的新感染数。利用发病率数据对(R_t)随时间变化的估计方法依赖于代间隔分布(G(t))，而(G(t))通常从经验数据或使用简单疫情模型的理论研究中获得。然而，对于在宿主群体或疾病表现方面存在异质性的系统，缺乏获取(G(t))的数据以及合适的通用方法。在这项工作中，我们使用数学模型来弥补这一差距。我们提出了一种通用方法，用于在任意 compartmental 模型提供的模型子隔间内部和之间获得繁殖数和代间隔分布的显式表达式。此外，我们给出了使用发病率数据评估这些繁殖数的适当表达式。为了突出这种方法的相关性，我们将其应用于巴西里约热内卢州各城市的 COVID - 19 传播情况。使用两个元种群模型，我们估计了繁殖数以及每个城市在所有其他城市病例产生中的贡献。
