Integrable discretizations of the SIR model

TL;DR

This paper develops integrable, structure-preserving discrete versions of the SIR epidemiological model, deriving exact solutions and conserved quantities, and explores their ultradiscretization, enhancing the understanding of discrete epidemic modeling.

Contribution

It introduces new integrable discretizations of the SIR model, providing conditions for integrability and methods to derive exact solutions and conserved quantities.

Findings

Discrete SIR models that conserve original quantities

Exact solutions for integrable discrete models

Ultradiscretizable discrete SIR model

Abstract

Structure-preserving discretizations of the SIR model are presented by focusing on the hodograph transformation and the conditions for integrability for their discrete SIR models are given. For those integrable discrete SIR models, we derive their exact solutions as well as conserved quantities. If we choose the parameter appropriately for one of our proposed discrete SIR models, it conserves the conserved quantities of the SIR model. We also investigate an ultradiscretizable discrete SIR model.