Estimation and outbreak detection with interval observers for uncertain discrete-time SEIR epidemic models

Abstract

According to the World Health Organization, infectious diseases are among the top ten causes of death worldwide. To prepare intervention strategies in a timely manner, tracking the evolution of these diseases is critical. For this purpose, public health services have access to noisy counts of infected people, which we use here to design a state estimator for a nonlinear discrete-time Susceptible-Exposed-Infected-Recovered (SEIR) epidemic model. We consider the practical case in which only sets of admissible values are known for the model's disturbances, uncertainties and parameters. Moreover, no bounds are available for the uncertain transmission rate from the ‘susceptible’ to the ‘exposed’ stage of the illness. We estimate the set of possible values of the state using an interval observer and characterise the stability and size of the estimation errors using linear programming. Furthermore, we propose an epidemic outbreak detector that leverages these state interval estimates. We demonstrate the observer's performance in numerical simulations.