Department of Health Behavior and Health Systems, School of Public Health, University of North Texas Health Science Center, Fort Worth, TX, United States of America.
School of Professional Studies, Northwestern University, Chicago, IL, United States of America.
PLoS One. 2021 Mar 11;16(3):e0247512. doi: 10.1371/journal.pone.0247512. eCollection 2021.
Compartmental models in epidemiology characterize the spread of an infectious disease by formulating ordinary differential equations to quantify the rate of disease progression through subpopulations defined by the Susceptible-Infectious-Removed (SIR) scheme. The classic rate law central to the SIR compartmental models assumes that the rate of transmission is first order regarding the infectious agent. The current study demonstrates that this assumption does not always hold and provides a theoretical rationale for a more general rate law, inspired by mixed-order chemical reaction kinetics, leading to a modified mathematical model for non-first-order kinetics. Using observed data from 127 countries during the initial phase of the COVID-19 pandemic, we demonstrated that the modified epidemic model is more realistic than the classic, first-order-kinetics based model. We discuss two coefficients associated with the modified epidemic model: transmission rate constant k and transmission reaction order n. While k finds utility in evaluating the effectiveness of control measures due to its responsiveness to external factors, n is more closely related to the intrinsic properties of the epidemic agent, including reproductive ability. The rate law for the modified compartmental SIR model is generally applicable to mixed-kinetics disease transmission with heterogeneous transmission mechanisms. By analyzing early-stage epidemic data, this modified epidemic model may be instrumental in providing timely insight into a new epidemic and developing control measures at the beginning of an outbreak.
compartmental 模型在流行病学中通过构建常微分方程来描述传染病的传播，这些方程用于量化通过 Susceptible-Infectious-Removed (SIR) 方案定义的亚群中疾病进展的速度。SIR compartmental 模型的经典速率定律假设，传染病的传播速度与传染病因子呈一级关系。本研究表明，这种假设并不总是成立，并为更一般的速率定律提供了理论依据，该速率定律受混合阶化学反应动力学的启发，从而导致了非一级动力学的修正数学模型。使用 COVID-19 大流行初始阶段来自 127 个国家的观测数据，我们证明了修正后的流行模型比基于经典一级动力学的模型更符合实际情况。我们讨论了与修正后的流行模型相关的两个系数：传播速率常数 k 和传播反应级数 n。虽然 k 由于其对外部因素的响应而在评估控制措施的有效性方面具有实用性，但 n 与传染病因子的内在特性（包括繁殖能力）更密切相关。修正后的 compartmental SIR 模型的速率定律通常适用于具有异质传播机制的混合动力学疾病传播。通过分析早期流行数据，该修正后的流行模型可能有助于及时深入了解新的流行病，并在疫情爆发初期制定控制措施。
