Combinatorial metaheuristics applied to infectious disease models

Fallas-Monge, Juan José; Chavarría-Molina, Jeffry; Alpízar-Brenes, Geisel

doi:10.1109/concapan.2016.7942337

Cited by 3 publications

(4 citation statements)

References 9 publications

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“…First, we determine upper and lower bounds for the uncertain input ζ t . Next we design an interval observer for the system (1)- (2). We prove the inclusion relation 0 ≤ x t ≤ x t ≤ x t , ∀t ≥ 0, and the asymptotic stability of the error bounds.…”

Section: Interval Observer Designmentioning

confidence: 99%

“…In this section we design an interval observer for the SEIR model (1)- (2). We assume here that neither β t nor its bounding values are available, which makes the estimation problem more complicated than in [18] but more realistic [12], [21], [22].…”

Section: Interval Observer Designmentioning

confidence: 99%

“…Mathematical modelling of epidemics has become an essential part in the sentinel role played by public health response planning and early outbreak detection systems [2]- [6]. Kermack and McKendrick proposed the first modern mathematical epidemiology models in [7]: a Susceptible-Infectious-Recovered (SIR) model was used to model the plague (London 1665-1666, Bombay 1906) and cholera (London 1865) epidemics.…”

Section: Introductionmentioning

confidence: 99%

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An Interval Observer for Discrete-Time SEIR Epidemic Models

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2018

2018 Annual American Control Conference (ACC)

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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.

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Section: Interval Observer Designmentioning

confidence: 99%

Section: Interval Observer Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An Interval Observer for Discrete-Time SEIR Epidemic Models

Degue

2018

2018 Annual American Control Conference (ACC)

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“…Mathematical modeling of epidemics plays a major role in organizing public health responses and developing early outbreak detection systems [3][4][5][6][7]. The first modern math-ematical epidemic model, i.e., susceptible-infectious-recovered (SIR), was proposed by Kermack et al in 1927 for cholera (London 1865) and plague epidemics (Bombay 1906, London 1665-1666) [8].…”

Section: Introductionmentioning

confidence: 99%

Design and Application of an Interval Estimator for Nonlinear Discrete-Time SEIR Epidemic Models

et al. 2022

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This paper designs an interval estimator for a fourth-order nonlinear susceptible-exposed-infected-recovered (SEIR) model with disturbances using noisy counts of susceptible people provided by Public Health Services (PHS). Infectious diseases are considered the main cause of deaths among the top ten worldwide, as per the World Health Organization (WHO). Therefore, tracking and estimating the evolution of these diseases are important to make intervention strategies. We study a real case in which some uncertain variables such as model disturbances, uncertain input and output measurement noise are not exactly available but belong to an interval. Moreover, the uncertain transmission bound rate from the susceptible towards the exposed stage is not available for measurement. We designed an interval estimator using an observability matrix that generates a tight interval vector for the actual states of the SEIR model in a guaranteed way without computing the observer gain. As the developed approach is not dependent on observer gain, our method provides more freedom. The convergence of the width to a known value in finite time is investigated for the estimated state vector to prove the stability of the estimation error, significantly improving the accuracy for the proposed approach. Finally, simulation results demonstrate the satisfying performance of the proposed algorithm.

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

Degue

2019

International Journal of Control

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Combinatorial metaheuristics applied to infectious disease models

Cited by 3 publications

References 9 publications

An Interval Observer for Discrete-Time SEIR Epidemic Models

An Interval Observer for Discrete-Time SEIR Epidemic Models

Design and Application of an Interval Estimator for Nonlinear Discrete-Time SEIR Epidemic Models

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

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