Within-host bacterial growth dynamics with both mutation and horizontal gene transfer.

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 solving 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 defining thresholds numbers (i.e. each strain's effective reproduction and each strain's transition threshold numbers), we first express conditions for the existence of non-trivial stationary states. We find 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, concerning the order in the set of strain's effective 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).