| Abstract: |
| Mathematical models, including differential equations and stochastic processes, have gained considerable attention for understanding the evolution of antibiotic resistance. However, most existing models assume standing genetic variation and do not consider the possibility of random or drug-induced mutation of reference bacterial strains. Therefore, we propose a pharmacokinetics/pharmacodynamics (PK/PD) continuous-time Markov chain considering the competition and mutation between sensitive and resistant bacteria within an infected host during treatment. The proposed model is approximated as a generalized birth-death process with immigration, allowing for explicit derivation of the probability that a resistant population establishes during treatment. In addition to capturing the stochasticity of novel emergence of a resistant bacterial strain, we explore the effects of different antibiotic modes of action, horizontal gene transfer, nutrient availability, and drug pharmacokinetics on antibiotic resistance. We find that replication-targeting (biostatic) drugs suppress resistance more than death-targeting (biocidal) drugs. Like prior works, we obtain maximized resistance at intermediate drug concentrations; however, the consideration of novel mutation magnifies the superiority of higher doses in preventing resistance emergence. Our general approach allows for numerically calculating resistant density distributions and first passage times, which can provide further advances in quantifying the likelihood of multi-drug resistance emergence. |
|