El Maroufy, Hamid; Lahrouz, Adil; Leach, P. G. L. Qualitative behaviour of a model of an SIRS epidemic: stability and permanence. (English) Zbl 1231.34083 Appl. Math. Inf. Sci. 5, No. 2, 220-238 (2011). Summary: We consider a classical model of a SIRS epidemic in an open population. The positivity and permanence are studied and explicit formulae are obtained by which the eventual lower bound of the density of infectives can be computed. The stability of the model is studied. We mainly use the Lyapunov functional to established the global stability of disease-free and endemic equilibrium points for both the deterministic and stochastic models. In addition we illustrate the dynamic behaviour of the deterministic and stochastic models via a numerical example. Cited in 3 Documents MSC: 34C60 Qualitative investigation and simulation of ordinary differential equation models 92D30 Epidemiology 37N25 Dynamical systems in biology 34D20 Stability of solutions to ordinary differential equations 34F05 Ordinary differential equations and systems with randomness PDF BibTeX XML Cite \textit{H. El Maroufy} et al., Appl. Math. Inf. Sci. 5, No. 2, 220--238 (2011; Zbl 1231.34083)