A class of nonlinear adaptive observers for SIR epidemic model

Abstract : Mathematical epidemic models describe the spread of an infectious disease in a host population. The SIR model, which is one of the simplest, is based on the representation of interactions between three compartments in the population: the number of susceptible, infective and recovered individuals. In this note, we study the problem of state estimation for such a model, subject to seasonal variations and uncertainties in the measured incidence rate (assuming continuous measurement), and design for this purpose a class of nonlinear adaptive observers. Asymptotic stability and ro-bustness with respect to variation rates are ensured by an appropriate choice of the observer gains as a function of the state estimate, through the use of the theory of input-to-output stability. Numerical experiments are presented to illustrate the method efficiency.
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Pierre-Alexandre Bliman, Denis Efimov, Rosane Ushirobira. A class of nonlinear adaptive observers for SIR epidemic model. ECC 2018 - European Control Conference, Jun 2018, Limassol, Cyprus. pp.6. ⟨hal-01724989⟩

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