Fig 6. Dependence of the extinction transition on population size and antimicrobial mode of action.

Extinction probability p₀ versus the ratio $\mathcal{R}=(g_S^{\prime }-f_S^{\prime })/g_S^{\prime }$ with biostatic or biocidal antimicrobial, for different carrying capacities K, either in the small-period regime, with T = 10^2.5 (A and B) or in the large-period regime, with T = 10⁵ (C). Markers: simulation results, calculated over 10³ realizations. Vertical dashed lines: predicted extinction thresholds, i.e. values of $\mathcal{R}$ such that T/2 = τ_S (A and B) or $t_R^a={\tau }_S$ (C). Solid lines (C): Analytical estimates of p₀ from Eq 1 (biostatic) or Eq 4 (biocidal). For K = 10² and 10³, the analytical predictions in the biostatic and biocidal case are confounded, while for K = 10⁴ we used two shades of green to show the slight difference (light: biostatic, dark: biocidal). Parameter values: μ₁ = 10⁻⁵, μ₂ = 10⁻³, f_S = 1, f_R = 0.9, f_C = 1, g_S = g_R = g_C = 0.1, and $g_S^{\prime }=0.1$ (biostatic) or $f_S^{\prime }=1$ (biocidal). All simulations start with 10 S microorganisms.