  Motivated by the classical Susceptible-Infected-Recovered (SIR) epidemic
models proposed by Kermack and Mckendrick, we consider a class of stochastic
compartmental dynamical systems with a notion of partial ordering among the
compartments. We call such systems unidirectional Mass Transfer Models (MTMs).
We show that there is a natural way of interpreting a uni-directional MTM as a
Survival Dynamical System (SDS) that is described in terms of survival
functions instead of population counts. This SDS interpretation allows us to
employ tools from survival analysis to address various issues with data
collection and statistical inference of unidirectional MTMs. In particular, we
propose and numerically validate a statistical inference procedure based on
SDS-likelihoods. We use the SIR model as a running example throughout the paper
to illustrate the ideas.
