In this article, the Lotka–Volterra model is analyzed to reduce the infection of a complex microbiote. The problem is set as an optimal control problem, where controls are associated to antibiotic or probiotic agents, or transplantations and bactericides. Candidates as minimizers are selected using the Maximum Principle and the closed loop optimal solution is discussed. In particular a 2d–model is constructed with four parameters to compute the optimal synthesis using homotopies on the parameters. It is extended to the 3d–case to provide a geometric frame to direct and indirect numerical schemes.