Controlling dynamics of a COVID--19 mathematical model using a parameter switching algorithm

TL;DR

This paper introduces a parameter switching algorithm to control COVID-19 model dynamics, enabling approximation of various attractors and offering a novel chaos control method that generalizes Parrondo's paradox.

Contribution

It presents a new parameter switching algorithm for controlling COVID-19 model dynamics, allowing approximation of attractors and extending chaos control techniques.

Findings

The PS algorithm can approximate all system attractors.

It can induce stable or chaotic behaviors through parameter switching.

The method generalizes Parrondo's paradox.

Abstract

In this paper the dynamics of an autonomous mathematical models of COVID-19 depending on a real parameter bifurcation, is controlled by switching periodically the parameter value. For this purpose the Parameter Switching (PS) algorithm is used. With this technique, it is proved that every attractor of the considered system can be numerically approximated and, therefore, the system can be determined to evolve along, e.g., a stable periodic motion or a chaotic attractor. In this way, the algorithm can be considered as a chaos control or anticontrol (chaoticization)-like algorithm. Contrarily to existing chaos control techniques which generate modified attractors, the obtained attractors with the PS algorithm belong to the set system attractors. It is analytically shown that using the PS algorithm, every system attractor can be expressed as a convex combination of some existing attractors. Moreover, is proved that the PS algorithm can be viewed as a generalization of Parrondo\textsc{\char13}s paradox.