Dynamics of a within-host drug resistance model with impulsive state feedback control

Bacterial resistance poses a major hazard to human health, and is caused by the misuse and overuse of antibiotics. Thus, it is imperative to investigate the optimal dosing strategy to improve the treatment effect. In this study, a mathematical model of antibiotic-induced resistance is presented to improve the antibiotic effectiveness. First, conditions for the global asymptotical stability of the equilibrium without pulsed effect are given according to the Poincare '-Bendixson Theorem. Second, a mathematical model of the dosing strategy with impulsive state feedback control is also formulated to reduce drug resistance to an acceptable level. The existence and stability of the order-1 periodic solution of the system are discussed to obtain the optimal control of antibiotics. Finally, our conclusions are confirmed by means of numerical simulations.