ABSTRACT
Antimicrobial resistance is a major threat to global health, in particular, new SARS-CoV-2 variants during the COVID-19 pandemic. Scheduling cycling therapies by targeting phenotypic states associated with specific mutations can help us to eradicate pathogenic variants. In this paper, we introduce a logistic switching model to mutation networks of collateral resistance. We found conditions for which the unstable zero-equilibrium of the logistic maps can be stabilized through a switching signal. That is, persistent populations can be eradicated through tailored switching regimes. Starting from an optimal-control formulation, the switching policies show their potential in the stabilization of the zero-equilibrium for dynamics governed by logistic maps. Simulation results show the applicability of Parrondo's Paradox to design cycling therapies against drug resistance.