Sparse identification of epidemiological compartment models with conserved quantities

TL;DR

This paper introduces a linear programming approach for sparse identification of epidemiological compartment models that ensures model interpretability, sparsity, and conservation of total population from timeseries data.

Contribution

It proposes a novel linear program formulation that incorporates conservation laws and sparsity constraints, improving model interpretability and accuracy over existing methods.

Findings

Successfully captures system dynamics with sparse models

Ensures conservation of total population in identified models

Outperforms standard sparse regression methods on synthetic data

Abstract

We investigate the application of a framework for sparse model identification of differential equations from timeseries data in the context of compartmental models in epidemiology. Such frameworks often seek a sparse representation from a polynomial basis in the state variables which reproduces the timeseries. Out-of-the-box approaches for the underlying sparse regression problem have moderate success reproducing the provided timeseries, but typically fail at producing a consistent, interpretable compartment model and conserving the total population, which are common properties in principled compartment modeling. Additionally, the conserved polynomial quantities, such as the sum of state variables, add algebraic nuances to a polynomial design matrix. We propose a linear program formulation to solve these issues by posing a pure one-norm objective, sampling from the nullspace of the design matrix, and imposing a set of linear constraints for between-compartment flows. We conduct several numerical experiments on synthetic data and succeed in ensuring model sparsity, accurately capturing system dynamics, and preserving conservation of population.