基本再生数 $R_0$ 在房室疾病模型中的结构
Structures of the Basic Reproduction Number $R_0$ Across Compartmental Disease Models
- University of Texas at San Antonio（圣安东尼奥德克萨斯大学）
- University of California, Berkeley（加州大学伯克利分校）
- Saint Mary’s Hall（圣玛丽学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出基本再生数 $R_0$ 的结构分类法，涵盖多种传播特征的房室模型，通过下一代矩阵法推导并解释其代数形式，统一不同推导，兼具研究综述与教学参考价值。
AI中文摘要：
基本再生数 $R_0$ 是数学流行病学中的核心无量纲量，它刻画了疾病暴发的阈值和流行病的早期增长率。在不同传播机制的模型中，$R_0$ 的代数形式差异很大，对其解释可以进一步提供关于传播动态和疾病干预的生物学见解。我们针对涵盖一系列疾病传播特征的房室常微分方程模型，提出了 $R_0$ 的结构分类法，这些特征包括分期进展、差异感染性、竞争菌株、媒介传播、性传播感染、反复感染、母体传播和基因驱动遗传。对于每个结构类别，我们提供了一个实例，通过下一代矩阵方法推导 $R_0$，并根据潜在传播途径解释所得代数表达式。通过将不同的推导统一在单一结构框架下，我们阐明了特定代数形式的 $R_0$ 何时以及为何出现。本综述既作为研究综合，也作为面向进入该领域的学生和研究人员的自成体系的教学参考。
英文摘要：
The basic reproduction number $R_0$ is the central dimensionless quantity in mathematical epidemiology, characterizing the threshold for disease outbreak and the early growth rate of an epidemic. The algebraic form of $R_0$ varies widely across models of distinct transmission mechanisms, and its interpretation can yield further biological insight into transmission dynamics and disease intervention. We present a structural taxonomy of $R_0$ for compartmental ordinary differential equation models spanning a range of disease transmission features, including staged progression, differential infectivity, competing strains, vector-borne transmission, sexually transmitted infection, recurrent infection, maternal transmission, and gene drive inheritance. For each structural class, we provide a worked example, deriving $R_0$ via the next-generation matrix approach and interpreting the resulting algebraic expression in terms of the underlying transmission pathway. By unifying disparate derivations under a single structural framework, we clarify when and why particular algebraic forms of $R_0$ arise. This review serves both as a research synthesis and as a self-contained pedagogical reference for students and researchers entering the field.
