An Interval Observer for Discrete-Time SEIR Epidemic Models

Abstract

This paper focuses on designing a state estimator for a discrete-time SEIR epidemic model of an influenzalike illness. It is assumed that only sets of admissible values are known for the model's disturbances, uncertainties and parameters, except for the time-varying transmission rate from the "susceptible" to the "exposed" stage, whose bounding values are unavailable. An interval observer is designed to estimate the set of possible values of the state, and a sufficient condition guaranteeing the asymptotic stability of the proposed estimator is formulated in terms of a linear matrix inequality. The performance of the proposed approach is demonstrated by numerical simulations.

Distributed model predictive control of positive Markov jump systems

“…Considering that the measured data and parameters contain numerous uncertainties, it is difficult to make a reasonable prediction based on the SEIR model with fixed values of parameters. Thus, an interval approach has already been applied to SEIR models in [49] and [50] .…”

“…The literature [47] , [48] , [49] , [50] was concerned with the modeling, the parameter identification of models, and the state estimation. These literature can provide some available modeling of SEIR and present some effective predict for the trend of epidemics.…”

“…It should be pointed out that the parameters in the considered system are not from a real case in some zone. In practice, one can utilize the methods in [47] , [48] , [49] , [50] to identify parameters by virtue of some real data. Then, the approach in this section can be used to contain epidemics.…”

Interval observer design for sequestered erythrocytes concentration estimation in severe malaria patients

“…Several approaches to design interval/set-membership estimators have been proposed [9,10,11,12,13,14]. This work is devoted to a subclass of set-membership estimators, the so-called interval observers, whose design is based on the monotone systems theory [15,12,16,17,18,19,20,21,22]. In contrast to [5], since the estimated variables take positive values, the obtained estimates provided by our observer take positive values only, which poses an additional constraint to satisfy in this rather complex estimation problem.…”

On a New Discrete SEIADR Model with Mixed Controls: Study of Its Properties

“…Also, an important computational work has been implemented to illustrate the validity of the obtained results. On the other hand, the design of the stabilizing controllers have been recently invoked and developed with a well-worked mathematical rigor in [36,37], respectively. Finally, a study of the nonlinear phenomena of bifurcation and chaos has been detailed in [38] for a discrete SI epidemic model with fractional order while [39] gives a relevance of the fractional framework to the statement of fractional-type discrete epidemic models especially through the list of commented listed "ad hoc" references.…”