An Introduction to Optimal Control Problems in Life Sciences and Economics

Aniţa, Sebastian; Arnăutu, Viorel; Capasso, Vincenzo

doi:10.1007/978-0-8176-8098-5

Cited by 94 publications

(84 citation statements)

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“…Among the classical books on the optimal control theory, we cite [8,9]. More recently, optimal control monographs specifically oriented to the solution of biological and epidemic problems appeared (see, e.g., [10,11]). …”

Section: Introductionmentioning

confidence: 99%

Optimal Control and Treatment of Infectious Diseases. The Case of Huge Treatment Costs

Liddo

2016

Mathematics

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Abstract:The representation of the cost of a therapy is a key element in the formulation of the optimal control problem for the treatment of infectious diseases. The cost of the treatment is usually modeled by a function of the price and quantity of drugs administered; this function should be the cost as subjectively perceived by the decision-maker. Nevertheless, in literature, the choice of the cost function is often simply done to make the problem more tractable. A specific problem is also given by very expensive therapies in the presence of a very high number of patients to be treated. Firstly, we investigate the optimal treatment of infectious diseases in the simplest case of a two-class population (susceptible and infectious people) and compare the results coming from five different shapes of cost functions. Finally, a model for the treatment of the HCV virus using the blowing-up cost function is investigated. Some numerical simulations are also given.

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Section: Introductionmentioning

confidence: 99%

Optimal Control and Treatment of Infectious Diseases. The Case of Huge Treatment Costs

Liddo

2016

Mathematics

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“…Our numerical results used the forward-backward sweep method, an it-erative algorithm to solve the optimality system, consisting of the state and adjoint equations and the optimal control characterization. For other solution approaches and numerical methods, see [1,3,17,43].…”

Section: Resultsmentioning

confidence: 99%

Illustrating Optimal Control Applications with Discrete and Continuous Features

Lenhart

Bodine

Zhong

et al. 2013

Advances in Applied Mathematics, Modeling, and Computational Science

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In this paper, we present the basic idea of optimal control of models with discrete and continuous features. We first consider ordinary differential equation (ODE) models where we emphasize problems which are linear in the control and have discrete values for the optimal control. Three examples with ODEs illustrate how the bang-bang and singular controls could be handled. The first example utilizes a simple model with one ODE. The next two examples use systems of ODEs. One example comes from a mobile robot with one or more steerable drive wheels that steer together. The other example models species augmentation where two populations of the same species are modeled with a target/endangered population and a reserve population. Then we present an extension to an integrodifference model that is discrete in time and continuous in space. This optimal pest control problem is modeled by integrodifference equations and we illustrate how to construct the necessary conditions.

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“…These steps are summarized in the Algorithm 1. More information on iterative approach can be obtained in [4,22]. and (c)), the circled black lines represent the variables run in the presence of control efforts described.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%