A drug taken orally is ingested at a rate r. The mass of the drug in the gastrointestinal tract is denoted by m1 and in the bloodstream by m2. The rate of change of the mass of the drug in the gastrointestinal tract is equal to the rate at which the drug is ingested minus the rate at which the drug enters the bloodstream, a rate that is taken to be proportional to the mass present. The rate of change of the mass in the bloodstream is proportional to the amount coming from the gastrointestinal tract minus the rate at which mass is lost by metabolism, which is proportional to the mass present in the blood. Develop a state space representation of this system.
For the special case where the coefficients of A are equal to 1 (with the appropriate sign), determine the response when m1(0) = 1 and m2(0) = 0. Plot the state variables versus time and on the x1 - x2 state plane.