A SEIR model for control of infectious diseases with constraints

Biswas, Md. Haider Ali; Paiva, Luís Tiago; Pinho, Maria do Rosário de

doi:10.3934/mbe.2014.11.761

Cited by 153 publications

(104 citation statements)

References 15 publications

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“…Such scientific exercise are of interest to compare different vaccination scenarios. In [13] and [1] different policies are confronted. However, in both such works, the cost of the optimal control problems considered is defined by an integrand quadratic with respect to control.…”

Section: Introductionmentioning

confidence: 99%

“…However, in both such works, the cost of the optimal control problems considered is defined by an integrand quadratic with respect to control. A special feature of [1] is that a somewhat realist scenario of limited supplies of vaccine at each instant is considered. From the point of view of optimal control, this is translated by the introduction of a mixed constraint (also known as state dependent control constraint).…”

Section: Introductionmentioning

confidence: 99%

“…Here, we propose the introduction of a cost of L 1 type which is linear with respect to the control variable. Our starting point is the recent work [1], where the number of vaccines at each time is assumed to be limited. This yields an optimal control problem with a mixed control-state constraint.…”

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confidence: 99%

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Optimal Control of a SEIR Model with Mixed Constraints and L 1 Cost

Pinho¹,

Корниенко²,

Maurer³

2015

Lecture Notes in Electrical Engineering

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Abstract. Optimal control can help to determine vaccination policies for infectious diseases. For diseases transmitted horizontally, SEIR compartment models have been used. Most of the literature on SEIR models deals with cost functions that are quadratic with respect to the control variable, the rate of vaccination. Here, we propose the introduction of a cost of L 1 type which is linear with respect to the control variable. Our starting point is the recent work [1], where the number of vaccines at each time is assumed to be limited. This yields an optimal control problem with a mixed control-state constraint. We discuss the necessary optimality conditions of the Maximum Principle and present numerical solutions that precisely satisfy the necessary conditions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal Control of a SEIR Model with Mixed Constraints and L 1 Cost

Pinho¹,

Корниенко²,

Maurer³

2015

Lecture Notes in Electrical Engineering

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“…Nowadays optimal control theory has received increasing importance in biomedical applications [ISN + 13, CL08,BPd14]. Such techniques have been applied to the control of the joint administration of analgesics and hypnotics in patients under general anesthesia.…”

Section: Introductionmentioning

confidence: 99%

Reference Tracking of Depth of Anesthesia Using Optimal Control

Almeida¹,

Paiva²,

Mendonça³

et al. 2015

2015 Proceedings of the Conference on Control and Its Applications

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Optimal control theory has gained increasing importance in biomedical applications, e.g., in the automatic administration of anesthetics during general anesthesia. In this context, one of the features that needs to be monitored is the depth of anesthesia. This is usually achieved by the joint administration of hypnotics and analgesics. The depth of anesthesia is quantified by the bispectral index that varies between 97.7% and 0%. This index should usually be kept at a reference level between 40% and 60% during surgeries with general anesthesia. In this contribution, we consider an open-loop control strategy to achieve this goal. In order to determine a suitable controller, we formulate a nonlinear optimal control problem and we solve it using direct methods. These methods have become increasingly useful when computing the numerical solution of an optimal control problem. Moreover, they are known to provide a very robust and general approach.

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“…A detailed background and survey on HIV/AIDS is described in [4] [5] [6] [7]. HIV mainly targets CD behavior [8]. Numerous mathematical models have been developed to identify the characteristics of human immunodeficiency virus [9] [10] [11].…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling Applied to Understand the Dynamical Behavior of HIV Infection

Sahani¹,

Biswas²

2017

OJMSi

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The study of viral dynamics of HIV/AIDS has resulted in a deep understanding of host-pathogenesis of HIV infection from which numerous mathematical modeling have been derived. Most of these models are based on nonlinear ordinary differential equations. In Bangladesh, the rate of increase of HIV infection comparing with the other countries of the world is not so high. Bangladesh is still considered to be a low prevalent country in the region with prevalence < 1% among MARP (Most at risk populations). In this paper, we have presented the current situation of HIV infection in Bangladesh and also have discussed the mathematical representation of a three-compartmental HIV model with their stability analysis. We have determined the basic reproduction number 0 R and shown the local and global stability at disease free and chronic infected equilibrium points. Also we have shown that if the basic reproduction number 0 1 R ≤ , then HIV infection is cleared from T cell population and it converges to disease free equilibrium point. Whereas if 0 1 R > , then HIV infection persists.

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A SEIR model for control of infectious diseases with constraints

Cited by 153 publications

References 15 publications

Optimal Control of a SEIR Model with Mixed Constraints and L 1 Cost

Optimal Control of a SEIR Model with Mixed Constraints and L 1 Cost

Reference Tracking of Depth of Anesthesia Using Optimal Control

Mathematical Modeling Applied to Understand the Dynamical Behavior of HIV Infection

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