Area Carracedo, Iván CarlosFernández Fernández, Francisco JavierNieto Roig, Juan JoséFernández Tojo, Fernando Adrián2024-07-122024-07-122022Math Meth Appl Sci. 2022;45:7451–7465http://hdl.handle.net/10347/34446We 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.eng© 2022 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons, Ltd. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly citedhttp://creativecommons.org/licenses/by/4.0/Compartmental epidemiological modelCOVID-19Digital twinStieltjes differential equationjournal article10.1002/mma.8252open access