A class of nonlinear adaptive observers for SIR epidemic model

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 robustness 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.