Interval observers for SIR epidemic models subject to uncertain seasonality

Resumo

Epidemic models describe the establishment and spread of infectious diseases. Among them, the SIR model is one of the simplest, involving exchanges between three compartments in the population, that represent respectively the number of susceptible, infective and recovered individuals. The issue of state estimation is considered here for such a model, subject to seasonal variations and uncertainties in the transmission rate. Assuming continuous measurement of the number of new infectives per unit time, a class of interval observers with estimate-dependent gain is constructed and analyzed, providing lower and upper bounds for each state variable at each moment in time. The dynamical systems that describe the evolution of the errors are monotonous. Asymptotic stability is ensured by appropriate choice of the gain components as a function of the state estimate, through the use of a common linear Lyapunov function. Numerical experiments are presented to illustrate the method. © Springer International Publishing AG 2017.

Ficha do documento

Tipo

Livro

Ano

2017

Instituição

Springer Verlag

Fonte

Repositório da FGV

Idioma

Inglês

Acesso

Acesso aberto

DOI

10.1007/978-3-319-54211-9_3

Identificador

oai:repositorio.fgv.br:10438/25273

Temas

Saúde

Palavras-chave

Interval observerLinear lyapunov functionsMathematical epidemiologyMonotone systemsSIR modelUncertain systemsAsymptotic stabilityDynamical systemsEstimationFunctionsLyapunov functionsNumerical methodsState estimationContinuous measurementsInterval observersLower and upper boundsNumerical experimentsTransmission ratesEpidemiologySaúdeMatemáticaDoenças transmissíveisEpidemias - Modelos matemáticosDoenças transmissíveis - Epidemiologia