It is clearly in the tradition of biologists to conceptualize the dynamical evolution of biological systems in terms of statetransitions
of biological objects. This paper is mainly concerned with (but obviously not limited too) the immunological
branch of biology and shows how the adoption of UML (Unified Modeling Language) state-transition diagrams can ease the
modeling, the understanding, the coding, the manipulation or the documentation of population-based immune software
model generally defined as a set of ordinary differential equations (ODE), describing the evolution in time of populations of
various biological objects. Moreover, that same UML adoption naturally entails a far from negligible representational
economy since one graphical item of the diagram might have to be repeated in various places of the mathematical model.
First, the main graphical elements of the UML state-transition diagram and how they can be mapped onto a corresponding
ODE mathematical model are presented. Then, two already published immune models of thymocyte behavior and time
evolution in the thymus, the first one originally conceived as an ODE population-based model whereas the second one as
an agent-based one, are refactored and expressed in a state-transition form so as to make them much easier to understand
and their respective code easier to access, to modify and run. As an illustrative proof, for any immunologist, it should be
possible to understand faithfully enough what the two software models are supposed to reproduce and how they execute
with no need to plunge into the Java or Fortran lines.