System equations

State variables in each system are rescaled to improve speed of obtaining numerical approximations. N_X describes the concentration of a strain, B_z describes the concentration of a bacteriocin and A_y describes the concentration of a quorum molecule. C_N, C_B and C_A are scaling factors:

Each model is represented as sets where N defines the number of strains, B defines the set of bacteriocins and A defines the set of QS systems. The following differential equations are used to represent each model.

Growth is modelled by Monod’s equation for growth limiting nutrient, S. μxmax defines the maximal growth rate of the strain and K_X defines the concentration of substrate required for half-maximal growth.

Killing by bacteriocin is defined by ω(Bz′), where ω_max defines the maximal killing rate which is set to 0 if the strain is insensitive. K_ω defines the concentration at which half-maximal killing occurs.

Induction or repression of bacteriocin expression by QS, is defined by k_B(z, y), where z defines the bacteriocin being expressed and y defines the quorum molecule regulating its expression. KB_max z is the maximal expression rate of the bacteriocin and KBz is the concentration of quorum molecule at which bacteriocin is half-maximal. n_z defines the cooperativity of the AHL binding.