Each cell divides at a rate set by logistic growth and survives a dose C only if its own effective MIC (minimum inhibitory concentration) exceeds it:
S(C) = 1 / (1 + (C / MIC_eff)^4)
MIC_eff = MIC0 · (1 + 7·r[^2 in combo mode])
dN/dt = r_g · N · (1 - N/K) · S(C)
- Antibiotic dose — concentration bathing the dish; cells whose resistance r doesn't push MIC_eff above it are killed.
- Mutation rate — probability each division produces a spontaneous resistance-increasing mutation (chromosomal resistance).
- Conjugation (HGT) rate — probability per second that two cells swap a resistance plasmid by horizontal gene transfer, independent of parentage.
- 2-drug combination — squares the resistance term, so a cell needs strong resistance to both mechanisms to survive — much harder to evolve by chance.
Real-world relevance: sub-lethal or inconsistent antibiotic dosing is one of the strongest drivers of resistance evolution in hospitals, farms and the community — exactly what antibiotic-stewardship programmes try to prevent.