As the support and stabilization of organ function is a major goal of treatment in the Intensive Care Unit (ICU), changes in the function of organ systems are an important indicator of the progression of the disease and recovery. This paper presents how to construct a model that describes changes in organ failure of ICU patients on a day-to-day basis. The model is based on the daily Sequential Organ Failure Assessment (SOFA) scores for six organ systems and predicts, for each of these organ systems, whether failure or recovery is due on the next day, using six logistic regression equations. The joint set of equations, extended with equations for predicting ICU discharge and death, constitutes a firstorder multivariate Markov model. We applied the procedure on a dataset and found that most types of organ failure are highly persistent.