Abstract—This paper discusses the optimization of customized intravenous-drip therapy regimens for individual patients infected with antibiotic-resistant bacteria, namely Extended-Spectrum-Beta-Lactamase (ESBL) bacteria. By utilizing Ordinary Differential Equations (ODE) to model the system’s dynamics, evaluated the efficiencies of the four most typical types of pulse functions, namely Dirac delta, sine, trapezoid, and normal distribution functions, as well as the time required for each treatment to suppress the pathogen population. The results revealed that a trapezoid pulse function for intravenous delivery of antibiotics is most favorable. Subsequently, infection severity was randomized by altering the bacterial and Beta-Lactamase population. The efficiency of each randomized regimen was evaluated using a predetermined score matrix that assessed the dosing length, dosing interval, maximum rate of antibiotic infusion, net consumption of antibiotics, and the total number of required treatments. Radar charts and box plot models were employed to present the findings. It was discovered that for more severely infected patients with a higher initial population and growth rate, it is important to decrease the time interval between subsequent doses and increase the time of maximum infusion rate. Conversely, for mild infections, the time interval between doses should be increased, and the time of maximum infusion rate should be decreased. It should be noted that maximizing the infusion rate does not enhance treatment efficiency. Furthermore, in comparison to the initial infected bacteria population size, the growth rate, and Bla production rate play more important roles in impacting treatment efficacy. 
 

Keywords—Collective Antibiotic Tolerance (CAT), Beta-Lactam antibiotics, Intravenous drip (IV-drip) therapy, Extended Spectrum Beta Lactamase (ESBL), Beta-Lactamase production rate, optimize treatment 

Cite: Irene Yicheng Jiang and Will Cao, "Customized and Optimized Treatment of Extended-Spectrum-Beta-Lactamase Bacteria for Individual Patients," International Journal of Pharma Medicine and Biological Sciences, Vol. 13, No. 1, pp. 1-13, 2024.

Copyright © 2024 by the authors. This is an open access article distributed under the Creative Commons Attribution License (CC BY-NC-ND 4.0), which permits use, distribution and reproduction in any medium, provided that the article is properly cited, the use is non-commercial and no modifications or adaptations are made.