Introducing State Constraints in Optimal Control for Health Problems

Корниенко, И. В.; Paiva, Luís Tiago; Pinho, Maria do Rosário de

doi:10.1016/j.protcy.2014.10.249

Cited by 9 publications

(9 citation statements)

References 10 publications

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“…In [13], the authors defined an isoperimetric constraint on the control variable only to model the total tolerable dosage amount of a therapy along the treatment period. In their conferences talks [26,27], Kornienko et al and De Pinho et al introduced state constraints in an optimal control problem that is subject to an S-Exposed-I-R differential system to model the situation of limited supply of vaccine based on work in [14] and where the isoperimetric constraint is defined on the product of the control and state variables.…”

Section: Free Horizon Isoperimetric Optimal Control Approachmentioning

confidence: 99%

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Time Needed to Control an Epidemic with Restricted Resources in SIR Model with Short-Term Controlled Population: A Fixed Point Method for a Free Isoperimetric Optimal Control Problem

Abouelkheir

Kihal

Rachik

et al. 2018

MCA

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In this paper, we attempt to determine the optimal duration of an anti-epidemic control strategy which targets susceptible people, under the isoperimetric condition that we could not control all individuals of this category due to restricted health resources. We state and prove the local and global stability conditions of free and endemic equilibria of a simple epidemic compartmental model devised in the form of four ordinary differential equations which describe the dynamics of susceptible-controlled-infected-removed populations and where it is taken into account that the controlled people cannot acquire long-lived immunity to move towards the removed compartment due to the temporary effect of the control parameter. Thereafter, we characterize the sought optimal control and we show the effectiveness of this limited control policy along with the research of the optimal duration that is needed to reduce the size of the infected population. The isoperimetric constraint is defined over a fixed horizon, while the objective function is defined over a free horizon present under a quadratic form in the payoff term. The complexity of this optimal control problem requires the execution of three numerical methods all combined together at the same time, namely, the forward–backward sweep method to generate the optimal state and control functions, the secant method adapted to the isoperimetric restriction, and, finally, the fixed point method to obtain the optimal final time.

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Section: Free Horizon Isoperimetric Optimal Control Approachmentioning

confidence: 99%

“…26.4081 (found at iteration 292) SIR dynamics with the precision of the optimal horizon t * f with the same parameters, initial conditions and severity weights constants as inFigure 1.…”

mentioning

confidence: 99%

Time Needed to Control an Epidemic with Restricted Resources in SIR Model with Short-Term Controlled Population: A Fixed Point Method for a Free Isoperimetric Optimal Control Problem

Abouelkheir

Kihal

Rachik

et al. 2018

MCA

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“…In [25,26], the authors defined an isoperimetric constraint on the control variable only, to model the total tolerable dosage amount of a therapy along the treatment period. In their conferences talks [28,29], Kornienko et al and de Pinho et al introduced state constraints in an optimal control problem that is subject to an S-exposed-I-Rdifferential system to model the situation of the limited supply of vaccine based on the work in [24] and where the isoperimetric constraint is defined on the product of the control and state variables. Our study aims to highlight more the importance of such optimal control approaches by considering a discrete model rather than a continuous one.…”

Section: N − 1}}mentioning

confidence: 99%

Optimal Control and Computational Method for the Resolution of Isoperimetric Problem in a Discrete-Time SIRS System

Kihal

Abouelkheir

Rachik

et al. 2018

MCA

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We consider a discrete-time susceptible-infected-removed-susceptible “again” (SIRS) epidemic model, and we introduce an optimal control function to seek the best control policy for preventing the spread of an infection to the susceptible population. In addition, we define a new compartment, which models the dynamics of the number of controlled individuals and who are supposed not to be able to reach a long-term immunity due to the limited effect of control. Furthermore, we treat the resolution of this optimal control problem when there is a restriction on the number of susceptible people who have been controlled along the time of the control strategy. Further, we provide sufficient and necessary conditions for the existence of the sought optimal control, whose characterization is also given in accordance with an isoperimetric constraint. Finally, we present the numerical results obtained, using a computational method, which combines the secant method with discrete progressive-regressive schemes for the resolution of the discrete two-point boundary value problem.

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“…Herewith, an accuracy can be obtained which is surely beyond the accuracy of the model, but gives almost as much inside as using a First-optimize-then-discretize method based on the full minimum principle and using a multipoint boundary value solver for the resulting multi-point boundary value problem with jump conditions. 10 We will not pursue these ideas furtheron. They would be inappropriate for the more qualitative models discussed here.…”

Section: Scenariomentioning

confidence: 99%

“…37, the other necessary conditions associated with the minimum principle can be checked, too, such as the sign of the multipliers associated with path constraints and the signs of the jumps occuring at the junction points of boundary arcs in case of pure state constraints; see[7], Theorem 4.1 and 4.2. See also[10].…”

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confidence: 99%

Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth

Thäter

Chudej

Pesch

2017

MBE

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In this paper an improved SEIR model for an infectious disease is presented which includes logistic growth for the total population. The aim is to develop optimal vaccination strategies against the spread of a generic disease. These vaccination strategies arise from the study of optimal control problems with various kinds of constraints including mixed control-state and state constraints. After presenting the new model and implementing the optimal control problems by means of a first-discretize-then-optimize method, numerical results for six scenarios are discussed and compared to an analytical optimal control law based on Pontrygin's minimum principle that allows to verify these results as approximations of candidate optimal solutions.

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Introducing State Constraints in Optimal Control for Health Problems

Cited by 9 publications

References 10 publications

Time Needed to Control an Epidemic with Restricted Resources in SIR Model with Short-Term Controlled Population: A Fixed Point Method for a Free Isoperimetric Optimal Control Problem

Time Needed to Control an Epidemic with Restricted Resources in SIR Model with Short-Term Controlled Population: A Fixed Point Method for a Free Isoperimetric Optimal Control Problem

Optimal Control and Computational Method for the Resolution of Isoperimetric Problem in a Discrete-Time SIRS System

Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth

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