We present a technique to model the biodegradation processes of carbamazepine (CBZ) using a system of ordinary differential equations. The CBZ is a pharmaceutical compound with low solubility utilised worldwide and an emerging contaminant. Its biodegradation was mediated by the microbial consortium BOS08 extracted from wood rot in an Atlantic Forest. The mathematical model is obtained as a set of ordinary diferential equations, where a Picard contraction mapping technique is used to fix the value of the parameters involved by solving the inverse problem. The technique offers a powerful tool for simulating, predicting, and developing future models allowing biodegradation optimisation.