Two coupled rates, updated every simulated hour:
dS/dt = -(μmax·f(T)·f(pH)·X·S/(Ks+S)) / Y
dX/dt = μmax·f(T)·f(pH)·X·S/(Ks+S) - kd·X
S is pollutant concentration, X is bacterial biomass (e.g. Pseudomonas-type degraders), Ks the half-saturation constant, Y the yield coefficient and kd the endogenous decay rate. f(T) and f(pH) are bell-shaped efficiency curves peaking near 30 °C and pH 7 — the population grows logistically while pollutant remains, then declines once its food source runs out.
- Higher inoculum → faster initial cleanup, same eventual total consumption.
- Temperature/pH far from optimum slow metabolism sharply.
- Bacteria (green spheres) cluster and multiply over the contamination patch, thinning out as it clears.