Bayesian Symbolic Regression for Infectious Disease Modeling Restricted; Files Only

Abstract

Understanding the transmission dynamics of infectious diseases is essential for

effective public health planning and intervention. Traditional epidemiological models,

such as the susceptible–infectious–recovered (SIR) framework rely on predefined

mechanistic equations derived from theoretical assumptions. However, specifying

the correct model structure can be challenging when the underlying transmission

mechanisms are complex or partially unknown.

In this study, we investigate the use of Bayesian Symbolic Regression (BSR) as a

data-driven approach for discovering dynamic equations governing infectious disease

transmission. The BSR framework employs reversible jump Markov chain Monte

Carlo (RJMCMC), the method simultaneously searches over model structures and

parameter values, allowing flexible identification of parsimonious equations that best

describe the observed dynamics.

We apply the proposed framework to both simulated epidemic data and historical

infectious disease datasets, including measles and chickenpox incidence time series.

The results demonstrate that Bayesian symbolic regression can successfully recover

underlying transmission relationships and produce interpretable models consistent

with established epidemiological theory. Compared with traditional approaches, the

method provides greater flexibility in discovering governing dynamics directly from

data while maintaining interpretability and providing insights into the mechanisms

underlying infectious disease transmission.

Table of Contents

1 Introduction 1

2 Models and Datasets 5

2.1 Classical epidemic models: SIR 5

2.2 Time-Series SIR Model (TSIR) 6

2.3 Datasets 8

3 Methods 14

3.1 Generic epidemic model formulation 14

3.2 Symbolic representation of transmission dynamics 15

3.3 RJMCMC proposal and acceptance mechanism 15

3.4 Prior specification 21

3.5 Likelihood specification 23

3.6 Posterior evaluation and model selection 23

3.7 Modification to the RJMCMC sampling strategy 24

3.8 Modification to the original BSR model selection strategy. 25

4 Results 26

4.1 Model rediscovery from simulated data 26

4.2 Model rediscovery from real data 27

4.3 Model prediction for jump steps 29

5 Discussion 30

Bibliography 32

List of Figures

2.1 London measles dynamics 9

2.2 Manchester measles dynamics 10

2.3 Liverpool measles dynamics 11

2.4 Birmingham measles dynamics 12

2.5 Ontario chickenpox dynamics 13

3.1 RJMCMC sampling workflow for Bayesian symbolic regression 16

4.1 Different jump steps for comparison 29

List of Tables

4.1 Recovered TSIR parameters from simulated data 27

4.2 TSIR parameters inferred by BSR from real incidence data 28

4.3 TSIR parameters inferred by BSR from real incidence data with seasonal

term 29

About this Master's Thesis

Rights statement

• Permission granted by the author to include this thesis or dissertation in this repository. All rights reserved by the author. Please contact the author for information regarding the reproduction and use of this thesis or dissertation.

School	Rollins School of Public Health
Department	Biostatistics
Subfield / Discipline	Biostatistics - MPH & MSPH
Degree	M.S.P.H.
Submission	Master's Thesis
Language	English
Research Field	Biology, Biostatistics
Keyword	SIR tsir infectious disease Bayesian Bayesian Symbolic Regression
Committee Chair / Thesis Advisor	Max Lau, Emory University
Committee Members	Yuke Wang, Emory University

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