Dynamic analysis of a bacterial resistance model with impulsive state feedback control

Bacterial resistance caused by prolonged administration of the same antibiotics exacerbates the threat of bacterial infection to human health. It is essential to optimize antibiotic treatment measures. In this paper, we formulate a simplified model of conversion between sensitive and resistant bacteria. Subsequently, impulsive state feedback control is introduced to reduce bacterial resistance to a low level. The global asymptotic stability of the positive equilibrium and the orbital stability of the order-1 periodic solution are proved by the Poincare-Bendixson Theorem and the theory of the semicontinuous dynamical system, respectively. Finally, numerical simulations are performed to validate the accuracy of the theoretical findings.