Switching Logistic Maps to Design Cycling Approaches Against Antimicrobial Resistance

Abstract

Antimicrobial resistance is a major threat to global health and food security today. Scheduling cycling therapies by targeting phenotypic states associated to specific mutations can help us to eradicate pathogenic variants in chronic infections. In this paper, we introduce a logistic switching model in order to abstract mutation networks of collateral resistance. We found particular conditions for which unstable zero-equilibrium of the logistic maps can be stabilized through a switching signal. That is, persistent populations can be eradicated through tailored switching regimens.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. However, employing such switching strategies, deserve a specific characterization in terms of limit behaviour. Ultimately, we use evolutionary and control algorithms to find either optimal and sub-optimal switching policies. Simulations results show the applicability of Parrondo's Paradox to design cycling therapies against drug resistance.

Scheduling collateral sensitivity‐based cycling therapies toward eradication of drug‐resistant infections

“…The dynamics of antibiotic resistance can be described using the following switched logistic system as proposed by: 42 $$$$ {\dot{x}}_i(t)={\rho}_{i,\sigma (t)}{x}_i(t)\left(1-\frac{x_i(t)}{K}\right)-{\delta}_{\sigma (t)}{x}_i(t)+\mu \sum \limits_{j\ne i}^n{m}_{ij,\sigma (t)}{x}_j(t) $$$$ defined for all $$$ t\ge 0, $$$ and $$$ {x}_i:i=1,2,3,\dots, n $$$. $$$ n $$$ represents different bacterial strains.…”