## Antimicrobial resistance

A generic within-host microbial dynamics model combining mutational processes, horizontal gene transfer and resource consumption. It describes interactions dynamics of four bacterial strains: one fully sensitive to the drug, one with mutational resistance only, one with plasmidic resistance only and one with both resistances. With respect to the order in the set of strain’s effective reproduction thresholds numbers, the qualitative dynamics of the model range from the extinction of all strains, coexistence of sensitive and mutational resistance strains to the coexistence of all strains at equilibrium (Djidjou-Demasse, Alizon & Sofonea).

This first approach (as many others in the large body of the literature) is based on assumption that antimicrobial efficacy is described by a single value, the minimal inhibitory concentration (MIC), which is the lowest concentration that prevents visible growth of the bacterial population. As a consequence, bacteria are then qualitatively categorized as resistant if therapeutic concentrations are below MIC and susceptible otherwise. However, antimicrobial resistance (AMR) is a continuous trait by nature referred to as antimicrobial quantitative resistance (qAMR). We tackle this issue by an integro-differential model formulation and introducing a real continuous phenotypic trait, describing the level of resistance. By simultaneously addressing the population and evolutionary dynamics, this approach does not ignore the evolutionary and epidemic short-term transient dynamics which lead to the emergence of resistance. Model’s typical dynamics is above. A: The basic reproduction numbers and without drug. B: Drug efficiency and the initial bacterial population. C: Time evolution of the total bacterial population. D: Distribution of the bacterial population with respect to time and resistance level. (Djidjou-Demasse, Sofonea, Choisy & Alizon).