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

Abstract

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.

Convergence Theorems for Varying Measures Under Convexity Conditions and Applications

“…where k is a fixed positive integer, the coefficients α j are strictly positive and (1) and if λ = lim n→∞ x n then x n ≤ kλ for all n ≥ 1.…”

“…Measure differential equations (which can be equivalently written as Stieltjes differential equations, see [19], [27]) proved themselves very useful in studying real life processes with dead times or abrupt changes occurring in their dynamics, e.g. [1], [19] or [29].…”

Finite-Interval Stability Analysis of Impulsive Fractional-Delay Dynamical System

“…Thereafter, the authors of [14] explored the FTS of a differential system with impulsive conditions by utilizing a delayed form of exponential function. Some recent noteworthy work on the FTS analysis of dynamical systems can be found in [30][31][32][33][34][35][36][37].…”

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“…The results of the study showed that awareness-raising controls could further reduce the number of COVID-19 infections. There are also many important literatures about COVID-19, please refer to [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] .…”