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

Area of Science:

• Mathematical Biology
• Control Theory
• Infectious Disease Dynamics

Background:

• Prolonged antibiotic use drives bacterial resistance, posing a significant public health threat.
• Current antibiotic treatment strategies require optimization to mitigate resistance development.
• Understanding bacterial population dynamics is key to developing effective interventions.

Purpose of the Study:

• To develop a mathematical model for bacterial sensitive-resistant conversion.
• To introduce an impulsive state feedback control strategy to reduce bacterial resistance.
• To analyze the stability of the bacterial population model under control.

Main Methods:

• Formulation of a simplified mathematical model for bacterial sensitive-resistant dynamics.
• Application of impulsive state feedback control to the bacterial model.
• Utilizing the Poincaré-Bendixson Theorem for global asymptotic stability analysis.
• Employing semi-continuous dynamical system theory for orbital stability analysis of periodic solutions.
• Conducting numerical simulations to verify theoretical results.

Main Results:

• The model demonstrates the conversion dynamics between sensitive and resistant bacterial populations.
• Impulsive state feedback control is shown to effectively reduce bacterial resistance levels.
• Global asymptotic stability of the positive equilibrium was proven.
• Orbital stability of the order-1 periodic solution was established.

Conclusions:

• The proposed impulsive control strategy offers a promising method for managing and reducing antibiotic resistance.
• Mathematical modeling and control theory provide powerful tools for optimizing antimicrobial therapies.
• Theoretical findings are validated by numerical simulations, supporting practical application.