# Inferring structure and parameters of stochastic reaction networks with logistic regression

## TL;DR

This paper introduces a method using logistic regression to infer the structure and parameters of chemical reaction networks from time-series data, with applications to epidemic models like SIR.

## Contribution

A novel likelihood-based approach using multinomial logistic regression to infer stoichiometries and network connectivity in stochastic reaction systems.

## Key findings

- Stoichiometric coefficients can be recovered when all species are observed and each reaction occurs at least once.
- The method successfully recovers network structure in catalytic and epidemic models like Togashi–Kaneko and SIR.
- The approach reliably estimates SIR parameters from synthetic data resembling real-world epidemics like COVID-19.

## Abstract

Identifying network structure and estimating reaction parameters remain central challenges in modeling chemical reaction networks. In this work, we develop likelihood-based methods that use multinomial logistic regression to infer both stoichiometries and network connectivity from full time-series trajectories of stochastic reaction systems. When molecular counts for all species are observed, stoichiometric coefficients can be recovered provided that each reaction occurs at least once during the sampling window and has a unique stoichiometric vector. We illustrate the proposed regression approach by recovering the network structure in three stochastic models involving catalytic interactions in open networks—namely, the Togashi–Kaneko model, a heat-shock protein network model, and a Susceptible–Infected–Recovered (SIR) epidemic model. We then demonstrate the practical value of the method using synthetic epidemic data designed to mirror key features of the COVID-19 outbreak in the Greater Seoul area of South Korea. In this example, we analyze an SIR network model with demographic effects and address partial observability—specifically, the fact that only infection counts are observed—by combining Bayesian logistic regression with differential-equation modeling. This integrated framework enables reliable recovery of core SIR parameters from a realistic, COVID-like synthetic trajectory of disease prevalence. Overall, our results show that relatively simple likelihood-based tools, such as logistic regression, can yield meaningful mechanistic insight from both synthetic systems and data that reflect real-world epidemic dynamics.