A Digital Twin of a Compartmental Epidemiological Model based on a Stieltjes Differential Equation

TL;DR

This paper develops a digital twin for the SIR epidemic model using Stieltjes derivatives, enabling real-time data integration and improved accuracy, demonstrated through COVID-19 simulations.

Contribution

It introduces a novel digital twin framework for epidemiological models based on Stieltjes differential equations, with theoretical analysis and real data validation.

Findings

The digital twin accurately replicates COVID-19 epidemic dynamics.

The model ensures existence and uniqueness of solutions.

Numerical simulations confirm real-time data integration improves predictions.

Abstract

We introduce a digital twin of the classical compartmental SIR (Susceptible, Infected, Recovered) epidemic model and study the interrelation between the digital twin and the system. In doing so, we use Stieltjes derivatives to feed the data from the real system to the virtual model which, in return, improves it in real time. As a byproduct of the model, we present a precise mathematical definition of solution to the problem. We also analyze the existence and uniqueness of solutions, introduce the concept of Main Digital Twin and present some numerical simulations with real data of the COVID-19 epidemic, showing the accuracy of the proposed ideas.