Résumé
The well-known SIR epidemic model is revisited. Continuous-time and discrete-time versions of an alternative model of this class are presented, discussed and validated with actual data. The proposed model follows from the calculation of the mean number of new infected cases due to the eventual meeting of susceptible and infected individuals, based on a simple probabilistic argument. Determination of the invariant set in the state space and convergence conditions towards equilibrium are established. For numerical analysis, data of daily number of new diagnosed cases provided by the Brazilian Ministry of Health and World Health Organization of COVID-19 outbreak that currently occurs respectively in Brazil and in the UK are used. Illustrations and model prediction analysis are provided and discussed from full data of both aforementioned countries which include more than 400 epidemic days. Three different and complementary strategies for parameter identification including the impact of causality on the optimal solution of the nonlinear mean square problem are discussed.