Structures of the Basic Reproduction Number R0 Across Compartmental Disease Models
Abstract
The basic reproduction number R0 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 R0 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 R0 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 R0 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 R0 arise. This review serves both as a research synthesis and as a self-contained pedagogical reference for students and researchers entering the field.
Related
- Reproduction number estimation using smoothing methods
- Impacts of ocean acidification and warming (OAW) on abalone growth and reproduction: A Dynamic Energy Budget model approach across SSP scenarios
- Stream and lake network position structures freshwater microbial communities across multiple catchments
- AlphaFold 3 Prediction Accuracy and Reliability across RNA Structures and Protein-RNA Interfaces
- Compartmental epidemiological models with infection-driven immune escape
BibTeX
@misc{qu2026structures,
title = {{Structures of the Basic Reproduction Number $R_0$ Across Compartmental Disease Models}},
author = {Zhuolin Qu and Abhi Ashwath},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13668},
eprint = {2609.13668},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13668},
}
RIS
TY - UNPB
TI - Structures of the Basic Reproduction Number R_0 Across Compartmental Disease Models
AU - Zhuolin Qu
AU - Abhi Ashwath
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.13668
UR - https://arxiv.org/abs/2609.13668
AB - 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.
ER -