Mathematical Models of Optimal Antibiotic Treatment

Abstract

When bacteria are exposed to antibiotics, the rate of killing can slow down dramatically over time. This phenomenon can be observed both in vitro and in vivo. In vitro, the mechanistic explanations for this can be divided into two main categories: antibiotic persistence and heteroresistance. In vivo, both mechanisms thought to contribute to observed slowdowns in the elimination and as a result may prolong the necessary treatment lengths. Therefore, by mitigating the slowdown it might be possible to shorten antibiotic treatments, however this is yet to be shown conclusively. This is also the case in tuberculosis when treatment regimens take at least 6 months. This thesis focuses on heteroresistance and its effects on the treatments lengths necessary to eliminate bacteria, particularly in the treatment of tuberculosis. To do so, I expand the mathematical toolbox of modeling heteroresistance on different scales, ranging from modeling chemical reaction kinetics to modeling multiple bacterial colonies within the tissues of patients. In addition, I analyzed clinical trials on high rifampicin doses in tuberculosis patients to show that heteroresistance the likely cause of the observed slowdown in elimination within the trial.