TABLE 1.

Equations used for model development^a

Model	Equation	Conditions
Cell growth of Lactobacillus sakei CTC 494	d[LAC]/dt = (μmax-LAC γi − Kd-LAC) [LAC]	t ≥ λLAC
	γi = 1	[LAC] < [LAC1]
	= 1 − I1 ([LAC] − [LAC1])	[LAC1] ≤ [LAC] ≤ [LAC2]
	= (1 − I1 ([LAC2] − [LAC1]) − I2 ([LAC] − [LAC2])	[LAC] > [LAC2]
Cell growth of the resistant Listeria subpopulation	d[LISR]/dt = (μmax -LISR − Kd−LISR) [LISR]	t ≥ λLISR
Cell growth of the sensitive Listeria subpopulation	d[LISS]/dt = (μmax-LISS − Kd-LISS) [LISS] − ψ [B] [LISS]	t ≥ λLISS
Bacteriocin activity	d[B]/dt = kBd[LAC]/dt − kinact [LAC] [B]	[LAC] ≥ [LACB]

^a[LAC] = cell concentration of Lactobacillus sakei CTC 494 (in CFU per ml), t = time (in hours), λ = lag phase (in hours), μ_max = maximum specific growth rate (per hour), K_d = specific death rate (per hour), γ_i = self-inhibition function for Lactobacillus sakei CTC 494, [LAC₁] and [LAC₂] = critical cell concentrations (in CFU per ml) where the subscripts refer to inhibition phases, I₁ and I₂ = corresponding inhibition coefficients, [LIS]_R = cell concentration of resistant Listeria innocua LMG 13568 (in CFU per ml), [LIS]_S = cell concentration of sensitive Listeria innocua LMG 13568 (in CFU per ml), ψ = bacteriocidal coefficient (in ml hours per AU), [B] = bacteriocin activity (in arbitrary units ml⁻¹), k_B = specific bacteriocin production (in AU per CFU), k_inact = apparent bacteriocin inactivation rate (in liters per CFU per hour), and [LAC_B] = minimum [LAC] for bacteriocin production, below which k_B equals 0 (in CFU per ml).