Compartmental models and competing risk

General compartmental models are derived using competing risk arguments. When the risk variables are exponential, the results specialize to the standard stationary Markov compartmental model. Iterative methods of solving the fundamental integral equation are given, and the uniqueness of the solution is incidentally established. The analysis is extended to include fixed inputs, orderly and nonorderly stream infusions, and time dependency. The study is motivated by a biological system that evolves through various stages over time.