The subject of this paper is the analysis of the equibria of a SIR
type epidemic model, which is taken as a case study among the wide family
of dynamical systems of infinite dimension. For this class of systems both
the determination of the stationary solutions and the analysis of their local
asymptotic stability are often unattainable theoretically, thus requiring the
application of existing numerical tools and/or the development of new ones.
Therefore, rather than devoting our attention to the SIR model’s features, its
biological and physical interpretation or its theoretical mathematical analysis,
the main purpose here is to discuss how to study its equilibria numerically, es-
pecially as far as their stability is concerned. To this end, we briefly analyze the
construction and solution of the system of nonlinear algebraic equations lead-
ing to the stationary solutions, and then concentrate on two numerical recipes
for approximating the stability determining values known as the characteristic
roots. An algorithm for the purpose is given in full detail. Two applications
are presented and discussed in order to show the kind of results that can be
obtained with these tools.
