It appears as if the failure of one organ system precipitates the subsequent failure of other organ systems. The aim of the present analysis is to model such system behavior and understand why medical complications accumulate in individual patients. The human body is first modeled as being comprised of multiple subsystems, with the health of each subsystem dependent on input regarding its own health status and that of all other subsystems. In a second step, the discrete model is generalized into a continuous model that captures system failure, as well as system repair, by a first order differential equation. Failure is approximated by a logistic decline and repair is approximated by a logistic rise in health. A small drop in health of a single subsystem spreads throughout the entire system and affects its overall health. Unless counteracted by measures of therapy or repair, any time-related loss in health of individual subsystems leads to a decline in health of the entire system. The delay in onset of therapy represents the most crucial factor to influence the overall cumulative decline in health. The model suggests that medical management needs to be expeditious to minimize the cumulative time-dependent toll of illness on the entire body.