Predicting the Duration of Antibacterial Treatment with Cell Wall Synthesis Inhibitors by using Mathematical Models

Abstract

This paper proposed a new mathematical model of within-host population dynamics of bacteria after cell wall synthesis inhibitors administration for practically predicting treatment duration and drug dosage. Our model deployed various concepts from different fields of probability, biology, physics, chemistry, pharmacology (pharmacokinetics and pharmacodynamics (PK/PD)), and medical sciences. The following assumptions and hypotheses were established: (i) binding or collision rate between drug molecule and bacteria depends on the relative velocity between drug molecule and bacteria, (ii) ability or probability of binding or capturing between drug molecule and bacteria can be evaluated by using four probability factors, based on the principal of physics and chemistry, (iii) the number of bacteria dying from antibiotics are equal to the number of drug molecules binding bacteria. Thus, bacterial death rate is equal to rate of drug molecules binding and killing bacteria (amount of drug molecules per second), and (iv) plasma drug concentration is constant and time-independent. The predicted result from our model was compared with the actual data of patient treatment and the classical Emax model derived from PK/PD models. The treatment duration with respect to drug administration of our result is closer to the actual patient treatment duration than the Emax model. It also preserves the similar recuperation rate as that of the real treatment.