Nonlinear observers: An application to the spread of an epidemic

The authors point out that the progress of an epidemic can be modeled by a mathematical process. In order to apply the required mathematical control engineering techniques, all the variables of the mathematical model describing the epidemic process have to be available from measurements. In the case where a variable or a parameter is not available for measurement, an observer has to be designed for estimating the unavailable state or parameter. For a nonlinear process, representing the spread of an epidemic, a nonlinear observer for estimating the rate at which susceptibles will develop the disease and become infective is proposed. The structure of the observer is simple and the simulations verify its good performance. Simulation results show good performance of the designed observer under noisy measurements and its ability to give an accurate estimate even in the case where the dynamical model is somewhat inaccurate