  The evolution and emergence of antibiotic resistance is a major public health
concern. The understanding of the within-host microbial dynamics combining
mutational processes, horizontal gene transfer and resource consumption, is one
of the keys to solve this problem. We analyze a generic model to rigorously
describe 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. By dening thresholds numbers (i.e. each
strain's eective reproduction and each strain's transition thresholds numbers),
we rst express conditions for the existence of non trivial stationary states.
We nd that these thresholds mainly depend on bacteria quantitative traits such
as nutrient consumption ability, growth conversion factor, death rate, mutation
(forward or reverse) and segregational loss of plasmid probabilities (for
plasmid-bearing strains). Next, with respect to the order in the set of
strain's eective reproduction thresholds numbers, we show that 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. Finally, we go through some applications of our general
analysis depending on whether bacteria strains interact without or with drug
action (either cytostatic or cytotoxic).
