Many bacteria have been observed to stop growing below a certain substrate threshold concentration. In this study, a modification of the Monod kinetics expression has been proposed to take into account this substrate threshold concentration observed in bacterial growth. Besides the threshold concentration no additional parameters have been added to the kinetic expression and so, only the substrate threshold concentration and the half-saturation constant have to be estimated for model calibration purposes. Furthermore, for parameter estimation purposes, practical identifiability of this new function has been studied and the results have been satisfactory. The new model has been applied, as an example, to a simple anaerobic model to simulate the competition for hydrogen between sulphate reducers and methanogens in a thermophilic methanol-fed bioreactor. Oscillatory behaviour and mathematical instabilities have been avoided by using the proposed model. Parameter sensitivities have also been calculated along the simulation period in order to investigate the importance of hydrogen threshold concentration parameters.