Abstract
Treatment of infectious diseases is often long and requires patients to take drugs even after they have seemingly recovered. This is because of a phenomenon called persistence, which allows small fractions of the bacterial population to survive treatment despite being genetically susceptible. The surviving subpopulation is often below detection limit and therefore is empirically inaccessible but can cause treatment failure when treatment is terminated prematurely. Mathematical models could aid in predicting bacterial survival and thereby determine sufficient treatment length. However, the mechanisms of persistence are hotly debated, necessitating the development of multiple mechanistic models. Here we develop a generalized mathematical framework that can accommodate various persistence mechanisms from measurable heterogeneities in pathogen populations. It allows the estimation of the relative increase in treatment length necessary to eradicate persisters compared to the majority population. To simplify and generalize, we separate the model into two parts: the distribution of the molecular mechanism of persistence in the bacterial population (e.g. number of efflux pumps or target molecules, growth rates) and the elimination rate of single bacteria as a function of that phenotype. Thereby, we obtain an estimate of the required treatment length for each phenotypic subpopulation depending on its size and susceptibility.