State estimators for some epidemiological systems

Iggidr, Abderrahman; Souza, Max O.

doi:10.1007/s00285-018-1273-3

Cited by 21 publications

(23 citation statements)

References 57 publications

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“…The stability of the equilibrium points of the epidemic models is an interesting topic which is of great relevance to healthcare management. See, for instance, [15][16][17][18][19]. Now, we discuss an epidemic based-model related to stabilization under the given framework of the Cauchy's interlacing theorem.…”

Section: Example Of Sir-type Epidemic Models Of Inter-community Clustersmentioning

confidence: 99%

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On Cauchy’s Interlacing Theorem and the Stability of a Class of Linear Discrete Aggregation Models Under Eventual Linear Output Feedback Controls

Sen

2019

Symmetry

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This paper links the celebrated Cauchy’s interlacing theorem of eigenvalues for partitioned updated sequences of Hermitian matrices with stability and convergence problems and results of related sequences of matrices. The results are also applied to sequences of factorizations of semidefinite matrices with their complex conjugates ones to obtain sufficiency-type stability results for the factors in those factorizations. Some extensions are given for parallel characterizations of convergent sequences of matrices. In both cases, the updated information has a Hermitian structure, in particular, a symmetric structure occurs if the involved vector and matrices are complex. These results rely on the relation of stable matrices and convergent matrices (those ones being intuitively stable in a discrete context). An epidemic model involving a clustering structure is discussed in light of the given results. Finally, an application is given for a discrete-time aggregation dynamic system where an aggregated subsystem is incorporated into the whole system at each iteration step. The whole aggregation system and the sequence of aggregated subsystems are assumed to be controlled via linear-output feedback. The characterization of the aggregation dynamic system linked to the updating dynamics through the iteration procedure implies that such a system is, generally, time-varying.

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Section: Example Of Sir-type Epidemic Models Of Inter-community Clustersmentioning

confidence: 99%

“…Thus, system (15), like (16), (17), can be interpreted as an aggregation model given by starting with the first cluster and successively incorporating the dynamics of the remaining clusters. Now, define the symmetric matrix M = M (N) = A T A.…”

Section: Example Of Sir-type Epidemic Models Of Inter-community Clustersmentioning

confidence: 99%

On Cauchy’s Interlacing Theorem and the Stability of a Class of Linear Discrete Aggregation Models Under Eventual Linear Output Feedback Controls

Sen

2019

Symmetry

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“…It turns out that controllability gramian of the pair (A 0 , b 0 ) is non-singular on [0, t * ] since the pair (A 0 , b 0 ) is controllable. Then, one gets from (9) and (12) that:…”

Section: Theoremmentioning

confidence: 99%

“…Such terms deviate the solution trajectory from the linear behavior about the equilibrium points. See, for instance, [5][6][7][8][9][10][11][12][13][14] and also [16][17][18][19][20][21] and some of the references therein. Example 1.…”

Section: Considerations On Reachability and Output Reachability In Somentioning

confidence: 99%

“…The background literature on epidemic models is very abundant, including the use of either vaccination or treatment controls as well as combinations of both types of controls. See, for instance, [5][6][7][8][9][10][11][12][13][14] and the references therein. Such controls may reduce the value of the basic reproduction number related to the case of absence of controls, so the average number of contagions per each primary infectious case, and they are also able to change the components of the equilibrium points, that is the numbers of each subpopulation at the equilibrium, and the rates the convergence to such equilibrium points.…”

Section: Introductionmentioning

confidence: 99%

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On the Approximated Reachability of a Class of Time-Varying Nonlinear Dynamic Systems Based on Their Linearized Behavior about the Equilibria: Applications to Epidemic Models

Sen

2019

Entropy

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This paper formulates the properties of point reachability and approximate point reachability of either a targeted state or output values in a general dynamic system which possess a linear time-varying dynamics with respect to a given reference nominal one and, eventually, an unknown structured nonlinear dynamics. Such a dynamics is upper-bounded by a function of the state and input. The results are obtained for the case when the time-invariant nominal dynamics is perfectly known while its time-varying deviations together with the nonlinear dynamics are not precisely known and also for the case when only the nonlinear dynamics is not precisely known. Either the controllability gramian of the nominal linearized system with constant linear parameterization or that of the current linearized system (which includes the time-varying linear dynamics) are assumed to be non-singular. Also, some further results are obtained for the case when the control input is eventually saturated and for the case when the controllability gramians of the linear parts are singular. Examples of the derived theoretical results for some epidemic models are also discussed.

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Nonlinear model predictive control with logic constraints for COVID-19 management

et al. 2020

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The management of COVID-19 appears to be a long-term challenge, even in countries that have managed to suppress the epidemic after their initial outbreak. In this paper, we propose a model predictive approach for the constrained control of a nonlinear compartmental model that captures the key dynamical properties of COVID-19. The control design uses the discrete-time version of the epidemic model, and it is able to handle complex, possibly time-dependent constraints, logical relations between model variables and multiple predefined discrete levels of interventions. A state observer is also constructed for the computation of non-measured variables from the number of hospitalized patients. Five control scenarios with different cost functions and constraints are studied through numerical simulations, including an output feedback configuration with uncertain parameters. It is visible from the results that, depending on the cost function associated with different policy aims, the obtained controls correspond to mitigation and suppression strategies, and the constructed control inputs are similar to real-life government responses. The results also clearly show the key importance of early intervention, the continuous tracking of the susceptible population and that of future work in determining the true costs of restrictive control measures and their quantitative effects.

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State estimators for some epidemiological systems

Cited by 21 publications

References 57 publications

On Cauchy’s Interlacing Theorem and the Stability of a Class of Linear Discrete Aggregation Models Under Eventual Linear Output Feedback Controls

On Cauchy’s Interlacing Theorem and the Stability of a Class of Linear Discrete Aggregation Models Under Eventual Linear Output Feedback Controls

On the Approximated Reachability of a Class of Time-Varying Nonlinear Dynamic Systems Based on Their Linearized Behavior about the Equilibria: Applications to Epidemic Models

Nonlinear model predictive control with logic constraints for COVID-19 management

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