Dynamic modeling is important to many areas of medical decision making. Cancer screening, infectious disease transmission, demographic modeling of healthcare and pension costs, economic growth, and budget forecasting provide a few arenas in which dynamic modeling plays a critical role. Differential or difference equations provide a framework for many of these problems.
In many cases, analysts can define differential equations that cannot be solved analytically at each moment in time. Fortunately, the long-term behavior of these systems can be explored or characterized through steady-state analysis.
This piece presents the basic character and limitations of steady-state analysis. It begins with some general background. It then discusses a specific steady-state analysis: the random-mixing model of infectious disease transmission in a population of injection drug users (IDUs).
Suppose one derives some ...