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.
This paper presents a new probabilistic dynamic model of the SIR class that describes, with appropriate precision, the temporal behavior of epidemics in discrete-time. Determination of the set of invariance 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 epidemic that currently occurs in Brazil is used. Illustrations and model prediction analysis are provided and discussed from full data of Italy, a country where the epidemic has already ended. The same ideas used on the development of the proposed model formulated in discrete-time may be adopted for continuous-time modelling as well. Three different and complementary strategies for parameter identification using the daily data available are considered.
com duração total de 30 horas, ofertado na FEEC/UNICAMP em uma versão emergencial devido à pandemia de COVID-19. O projeto emprega um módulo de som USB como alternativa financeiramente viável ao uso do osciloscópio e gerador de sinais. As topologias de amplificadores de sinais de áudio propostas devem receber sinais, processá-los e reproduzi-los em um alto-falante e, as formas de onda dos circuitos podem ser visualizadas no computador utilizando o módulo de som USB associado ao uso do software SoundCardOscilloscope (por Christian Zeitnitz). O projeto emprega circuitos elétricos fundamentais, amplamente estudados nas disciplinas teóricas de eletrônica, bem como conceitos incorporados em muitos equipamentos eletrônicos. Foram enviados kits para a residência de cada aluno, cujo custo total foi estimado
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