Learning Epidemic Threshold Equations from Simulation: REEBLRA, an Interpretable Bayesian Classification Framework for Reproduction Numbers
Abstract
The basic reproduction number, R0, is central to infectious-disease modelling, yet analytic expressions can be difficult to derive for high-dimensional, nonlinear, or structurally complex models. We introduce REEBLRA (R0 Equation Estimation using Bayesian Logistic Regression Algorithm), an interpretable framework that learns explicit surrogate equations for epidemic thresholds from parameter--response data. Rather than directly regressing R0, REEBLRA estimates Pr{R0(θ)>c} for parameter vector θ and threshold c. It provides a binary equation for classifying epidemic invasion (R0>1) and successive threshold equations defining ordered brackets that approximate R0, the expected number of secondary infections caused by a typical case in a fully susceptible population. The resulting equations support parameter screening, sensitivity interpretation, threshold classification, and exploratory analysis when analytic derivation is cumbersome. Bayesian logistic regression using standardized polynomial-like features and proper weakly informative priors yields regularized estimates, posterior uncertainty, and finite coefficients under complete or quasi-complete separation. We establish a mechanistic--surrogate concordance principle linking the full fitted-score gradient to the local gradient of log R0 under explicit regularity and tangency assumptions, allowing conditional interpretation of threshold directions. Across seven analytic-label benchmarks associated with ODE models, including a 15-compartment five-group SIR system, five-fold binary AUC was 0.999--1.000 and ordered-bracket accuracy was 0.951--0.998. REEBLRA complements rather than replaces mechanistic derivations, bridging simulation, machine learning, and reproduction-number analysis. An accompanying Shiny app supports implementation.
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BibTeX
@misc{rabajante2026learning,
title = {{Learning Epidemic Threshold Equations from Simulation: REEBLRA, an Interpretable Bayesian Classification Framework for Reproduction Numbers}},
author = {Jomar F. Rabajante and Norvin P. Bansilan and Maria Czarina T. Lagura-Arreza and Destiny SM. Lutero and Emerson R. Rico},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29399},
eprint = {2610.29399},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29399},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Learning Epidemic Threshold Equations from Simulation: REEBLRA, an Interpretable Bayesian Classification Framework for Reproduction Numbers
AU - Jomar F. Rabajante
AU - Norvin P. Bansilan
AU - Maria Czarina T. Lagura-Arreza
AU - Destiny SM. Lutero
AU - Emerson R. Rico
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29399
UR - https://arxiv.org/abs/2610.29399
AB - The basic reproduction number, R_0, is central to infectious-disease modelling, yet analytic expressions can be difficult to derive for high-dimensional, nonlinear, or structurally complex models. We introduce REEBLRA (R_0 Equation Estimation using Bayesian Logistic Regression Algorithm), an interpretable framework that learns explicit surrogate equations for epidemic thresholds from parameter--response data. Rather than directly regressing R_0, REEBLRA estimates Pr{R_0(θ)>c} for parameter vector θ and threshold c. It provides a binary equation for classifying epidemic invasion (R_0>1) and successive threshold equations defining ordered brackets that approximate R_0, the expected number of secondary infections caused by a typical case in a fully susceptible population. The resulting equations support parameter screening, sensitivity interpretation, threshold classification, and exploratory analysis when analytic derivation is cumbersome. Bayesian logistic regression using standardized polynomial-like features and proper weakly informative priors yields regularized estimates, posterior uncertainty, and finite coefficients under complete or quasi-complete separation. We establish a mechanistic--surrogate concordance principle linking the full fitted-score gradient to the local gradient of log R_0 under explicit regularity and tangency assumptions, allowing conditional interpretation of threshold directions. Across seven analytic-label benchmarks associated with ODE models, including a 15-compartment five-group SIR system, five-fold binary AUC was 0.999--1.000 and ordered-bracket accuracy was 0.951--0.998. REEBLRA complements rather than replaces mechanistic derivations, bridging simulation, machine learning, and reproduction-number analysis. An accompanying Shiny app supports implementation.
ER -