Lyapunov-based Switching to Mitigate Antimicrobial Resistance

Drug resistant pathogens are a global public health threat and their control have become a challenging task. In this paper, a mathematical model which describes the general dynamics of microbial resistance is employed. Utilizing a two-strain bacterial population, notions from control engineering and positive switched systems are used to develop control strategies aimed at minimizing the appearance of drug resistant bacteria within the host. Based on the Lyapunov function argument, a switching strategy can be found to ensure stability of the eradication equilibrium under given conditions. Numerical simulations compare switching under different feedback controls and validate the use of the switching strategy in general for the proposed model of bacterial resistance mitigation.