On the estimation of sequestered infected erythrocytes in &lt;em&gt;Plasmodium falciparum&lt;/em&gt; malaria patients

Bichara, Derdei; Cozic, Nathalie; Iggidr, Abderrahman

doi:10.3934/mbe.2014.11.741

Cited by 16 publications

(28 citation statements)

References 20 publications

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“…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]. First, we determine upper and lower bounds for the uncertain input ζ t .…”

Section: Interval Observer Designmentioning

confidence: 99%

“…Importantly, [18] assumed that the time-varying transmission rate β(t) from the "susceptible" to the "exposed" stage is bounded by two functions β(t) and β(t), available to the PHS in real-time. The time-varying observer proposed in [18] provided accurate results in simulated models, but the transmission rate β(t) is a highly uncertain parameter that cannot be estimated by biological considerations [21], [22] and its bounds are generally unknown in epidemiology models [12]. Here, we assume that neither the value of β(t) nor its bounding values are available, which makes the estimation problem more complicated.…”

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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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: Introductionmentioning

confidence: 99%

An Interval Observer for Discrete-Time SEIR Epidemic Models

Degue

2018

2018 Annual American Control Conference (ACC)

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“…With representation (1), y is not a state component, contrary e.g. to [3,5]. One sees easily that with this output, the system is detectable, but not observable at the disease-free equilibrium (where I = 0).…”

Section: Hypotheses On the Model And Preliminariesmentioning

confidence: 99%

Interval Observers for SIR Epidemic Models Subject to Uncertain Seasonality

Bliman

Barros

2017

Positive Systems

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Epidemic models describe the establishment and spread of infectious diseases. Among them, the SIR model is one of the simplest, involving exchanges between three compartments in the population, that represent respectively the number of susceptible, infective and recovered individuals. The issue of state estimation is considered here for such a model, subject to seasonal variations and uncertainties in the transmission rate. Assuming continuous measurement of the number of new infectives per unit time, a class of interval observers with estimate-dependent gain is constructed and analyzed, providing lower and upper bounds for each state variable at each moment in time. The dynamical systems that describe the evolution of the errors are monotonous. Asymptotic stability is ensured by appropriate choice of the gain components as a function of the state estimate, through the use of a common linear Lyapunov function. Numerical experiments are presented to illustrate the method.

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“…That is why the estimation of sequestered parasite population has been a challenge for the biologist and modeler, with many authors having studied this problem [10], [9], [15], [2]. In this work an interval observer is designed in order to estimate the admissible interval for sequestered parasite population.…”

Section: Kh Degue Is With the Department Of Electrical Engineeringmentioning

confidence: 99%

Interval estimation of sequestered infected erythrocytes in malaria patients

Degue¹,

Efimov²,

Iggidr³

2016

2016 European Control Conference (ECC)

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The problem of estimation of sequestered parasites Plasmodium falciparum in malaria, based on measurements of circulating parasites, is addressed. It is assumed that all (death, transition, recruitment and infection) rates in the model of a patient are uncertain (just intervals of admissible values are given) and the measurements are subject to a bounded noise, then an interval observer is designed. Stability of the observer can be verified by a solution of LMI. The efficiency of the observer is demonstrated in simulation.

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On the estimation of sequestered infected erythrocytes in <em>Plasmodium falciparum</em> malaria patients

Cited by 16 publications

References 20 publications

An Interval Observer for Discrete-Time SEIR Epidemic Models

An Interval Observer for Discrete-Time SEIR Epidemic Models

Interval Observers for SIR Epidemic Models Subject to Uncertain Seasonality

Interval estimation of sequestered infected erythrocytes in malaria patients

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