Numerical recipes for investigating endemic equilibria of age-structured SIR epidemics

The subject of this paper is the analysis of the equibria of a SIR \udtype epidemic model, which is taken as a case study among the wide family \udof dynamical systems of innite dimension. For this class of systems both \udthe determination of the stationary solutions and the analysis of their local \udasymptotic stability are often unattainable theoretically, thus requiring the \udapplication of existing numerical tools and/or the development of new ones. \udTherefore, rather than devoting our attention to the SIR model’s features, its \udbiological and physical interpretation or its theoretical mathematical analysis, \udthe main purpose here is to discuss how to study its equilibria numerically, es- \udpecially as far as their stability is concerned. To this end, we briey analyze the \udconstruction and solution of the system of nonlinear algebraic equations lead- \uding to the stationary solutions, and then concentrate on two numerical recipes \udfor approximating the stability determining values known as the characteristic \udroots. An algorithm for the purpose is given in full detail. Two applications \udare presented and discussed in order to show the kind of results that can be \udobtained with these tools