A class of nonlinear state observers for an SIS system counting primo-infections.

Observation and identification are important issues for the practical use of compartmental models of epidemic dynamics. They are usually evaluated based on the number of infected individuals (the prevalence) or the newly infected cases (the incidence). We are interested in a general question: may the measure of the number of primo-infected individuals and the prevalence improve state estimation? To study this question, we analyze in this paper a simple model of infection with waning immunity and, consequently, the possibility of reinfections. A class of nonlinear observers is built for this model, and tractable sufficient conditions on the gain matrices are established, ensuring asymptotic convergence of the state estimate towards its actual value. Numerical simulations illustrate the method.