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.

在本文中，我们提出了一个非线性数学模型，该模型描述了利用真菌将有机污染物生物降解的过程，并利用葡萄糖来维持其代谢和生长。从两个方面进行了研究，首先，我们研究了该模型的平衡及其稳定性，并分析了一些模型参数对持久平衡的敏感性。其次，调用最佳控制理论以提供一种最佳策略，以使污染物和真菌排放物保持接近于零，并以最佳方式允许通过喂入污染物使植物连续活动。一些数值模拟说明了理论结果。