A minimal cardiac model has been developed that captures the major dynamics of the cardio-vascular system (CVS). This model is extended to simulate time varying disease state including reflex actions and an integral based identification method is presented that enables linear and convex parameter identification. Two common time varying disease states are identified to within 10% without false identification. Also the valve law in this model is reformulated in terms of Heaviside functions, and a unique closed form analytical solution is obtained for the ventricular interaction equation. This enables rapid forward simulations of the model. Clinically, the method ensures medical staff can rapidly obtain a patient specific model and can simulate a large number of therapy combinations to find the best treatment