Abstract
Results of previous work on componentwise asymptotic stability (characterizations
based on the flow-invariance method) are applied for the study of a class of bilinear differential
equations, describing the dynamics of (compartmental) endemic epidemic systems. Using the
standard form of a SIR model, a necessary and sufficient condition is formulated for the
componentwise absolute stability on a given closed and bounded set, which includes the
equilibrium point of the system. It is shown that the class of approachable sets can be considerably
enlarged, by applying adequate bijective transformations of the original coordinates, used for the
initial statement of the problem. A detailed example illustrates the whole procedure for the
exploration of the componentwise absolute stability on a set resulting from a nonsingular linear
transformation applied to the original state variables.
