Concept and solution of digital twin based on a Stieltjes differential equation

We introduce the concept of a digital twin by using Stieltjes differential equations. A precise mathematical definition of solution to the problem is presented. We also analyze the existence and uniqueness of solutions, introduce the concept of main digital twin. As a particular case, the classical compartmental SIR (susceptible, infected, recovered) epidemic model is considered and we 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. Numerical simulations with real data of the COVID-19 epidemic show the accuracy of the proposed ideas.

Automated summary

This paper introduces the concept of a digital twin using Stieltjes differential equations and presents a precise mathematical definition of the solution to the problem. The existence and uniqueness of solutions are also analyzed and the concept of the main digital twin is introduced. Using the classical SIR epidemic model as an example, the interrelation between the digital twin and the system is studied, and Stieltjes derivatives are used to feed real system data to the virtual model, improving it in real time. Numerical simulations with real COVID-19 epidemic data demonstrate the accuracy of the proposed ideas.