📝 SummarXiv

Abstract

Antibiotic resistance presents a growing global health threat by diminishing the effectiveness of treatments and allowing once-manageable bacterial infections to persist. This study develops and analyzes an optimization-based mathematical model to investigate the impact of varying antibiotic dosages on bacterial resistance, incorporating the role of the immune system. Additionally, to capture the effects of over and underdosing, a floor function is newly introduced into the model as a switch function. The model is examined both analytically and numerically. As part of the analytical solution, the validity of the model through the existence and uniqueness theorem, stability at the equilibrium points, and characteristics of equilibrium points in relation to state variables have been investigated. Numerical simulations, performed using the Runge Kutta 4th order method, reveal that while antibiotics effectively reduce sensitive bacteria, they simultaneously increase resistant strains and suppress immune cell levels. The results also demonstrate that underdosing antibiotics increases the risk of resistance through bacterial mutation, while overdosing weakens the immune system by disrupting beneficial microbes. These findings emphasize that improper dosing whether below or above the prescribed level can accelerate the development of antibiotic resistance, underscoring the need for carefully regulated treatment strategies that preserve both antimicrobial effectiveness and immune system integrity.