Optimizing biological wastewater treatment

In this paper we propose a non linear mathematical model describing the process of biodegradation of organic pollutants by means of fungi, and using glucose to sustain its metabolism and growth. Two aspects are investigated, firstly, we study equilibria and their stability for this model, and analyze the sensitivity of the persistence equilibrium with respect to some model parameters. Secondly, optimal control theory is invoked to provide an optimal strategy for keeping pollutant and fungi effluents close to zero, and permitting a continuous activity of the plant by feeding pollutant, in an optimal way. Some numerical simulations illustrate the theoretical results.