Quantitative biology of survival under antibiotic treatments

The mathematical formulation for the dynamics of growth reduction and/or killing under antibiotic treatments has a long history. Even before the extensive use of antibiotics, attempts to model the killing dynamics of biocides were made [1]. Here, we review relatively simple quantitative formulations of the two main modes of survival under antibiotics, resistance and tolerance, as well as their heterogeneity in bacterial populations. We focus on the two main types of heterogeneity that have been described: heteroresistance and antibiotic persistence, each linked to the variation in a different parameter of the antibiotic response dynamics. Finally, we review the effects on survival of combining resistance and tolerance mutations as well as on the mode and tempo of evolution under antibiotic treatments.