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

Abstract

In this paper, the dynamics of an autonomous mathematical model of COVID‐19 depending on a real bifurcation parameter is controlled by the parameter switching (PS) algorithm. 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, for example, a stable periodic motion or a chaotic attractor. In this way, the algorithm can be considered as a chaos control or anticontrol (chaoticization) algorithm. Contrarily to existing chaos control techniques that generate modified attractors, the obtained attractors with the PS algorithm belong to the set of the 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. Interestingly, the PS algorithm can be viewed as a generalization of Parrondo's paradox.