Fig. 1

Conditions for plasmid persistence and elimination. a The concept of resistance reversal. A population initially consists of a mixture of sensitive (blue) and resistant (orange with plasmid) cells. In the presence of antibiotics (± indicates presence or absence of [A] antibiotic concentration), resistant cells are selected for. In the absence of antibiotics, as long as the plasmid imposes a fitness cost, then over a sufficiently long time the resistant cells will be presumably outcompeted, effectively reversing resistance. b Modeling plasmid dynamics in a single species (S). The plasmid-free population, S ⁰, acquires the plasmid through conjugation at a rate constant \(\eta _{\mathrm{C}}\), becoming S ¹. S ¹ reverts to S ⁰ through plasmid loss at a rate constant κ. S ⁰ grows at a rate proportional to S ¹ (μ ₁ = μ, μ ₀ = αμ). The plasmid is costly when α > 1 and beneficial when α < 1. Both populations turnover at a constant dilution rate D. c Simulated fraction of S ¹ as a function of α and \({\eta _{\rm C}}\) after 5000 time units (~200 days). Fast conjugation can compensate for plasmid loss even if the plasmid carries a cost (α > 1). A greater \({\eta _{\rm C}}\) is required to maintain the plasmid population as α increases. d Criterion for plasmid persistence. If \({\eta _{\rm C}}\) > \({\eta _{\rm Crit}} = \alpha \left( {\kappa + D} \right) - D\), the plasmid will dominate (Eq. (1))