Observation and identification are crucially important for the practical use of compartmental models in epidemiology. Typically, the state and parameters of the epidemic model are evaluated based on the number of infected individuals (prevalence) or the newly infected cases per time unit (incidence). However, when reinfections are possible, additional data such as the number of primary infections are retrievable. In this note, we investigate whether measuring the number of primary infections can improve estimation. To do so, we present several nonlinear adaptive observers for a simple infection model with waning immunity and subsequent reinfections. We then prove the practical asymptotic stability of the estimation errors using the Lyapunov function method. Finally, we illustrate the efficacy of the observers via simulations.