Observer design for SEIR discrete-time epidemic models

This paper presents the design of a state-observer for a discrete-time SEIR epidemic model. The model is obtained by discretizing a continuous-time one by using the Micken´s non-standard method. This procedure provides an implicit system of difference equations. The observer is then designed in an implicit way instead of obtaining first an explicit model of the system. Moreover, some sufficient conditions to ensure the asymptotic stability of the observer are provided in terms of a matrix inequality that can be cast into a LMI. The feasibility of the matrix inequality is stated while some simulation examples show the operation and usefulness of the observer.