The Analysis of a Mathematical Model Associated to an Economic Growth Process

Bundău, Olivia; Pater, Flavius; Juratoni, Adina

doi:10.1063/1.3241512

Cited by 4 publications

(3 citation statements)

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“…In what following we will determine the necessary conditions for optimal problem P as in [1], [2], [4]. To do this we will apply the principle of Pontryagin.…”

Section: Determination Of Optimality Conditionsmentioning

confidence: 99%

Optimal Conditions for the Control Problem Associated to a Biomedical Process

Bundău¹,

Juratoni²,

Chevereşan³

et al. 2010

AIP Conference Proceedings

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This paper considers a mathematical model of infectious disease of SIS type. We will analyze the problem of minimizing the cost of diseases trough medical treatment. Mathematical modeling of this process leads to an optimal control problem with a finite horizon. The necessary conditions for optimality are given. Using the optimality conditions we prove the existence, uniqueness and stability of the steady state for a differential equations system.

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“…In what following we will determine the necessary conditions for optimal problem P as in [1], [2], [4]. To do this we will apply the principle of Pontryagin.…”

Section: Determination Of Optimality Conditionsmentioning

confidence: 99%

Optimal Conditions for the Control Problem Associated to a Biomedical Process

Bundău¹,

Juratoni²,

Chevereşan³

et al. 2010

AIP Conference Proceedings

Self Cite

View full text Add to dashboard Cite

show abstract

“…These analyses aim at describing the structure of the optimal controls when the parameters of the model vary over some range. For example, Krasovskii and Tarasyev (2008) provide a qualitative analysis of the optimal solution of a general economic growth model (see also Bundău et al, 2009); LaTorre et al (2020) analyse the effects of different interventions in a simple macroeconomic epidemiological model, Baker et al (2019) analyse the structure of optimal management of invasive species, and Aseev et al (2005) study the optimal investments in an R&D model. Moreover, Aseev and Manzoor (2018) qualitatively characterize the solutions of an optimal harvesting problem with logistic growth: Assuming an effort‐based consumption model where utility is strictly concave in the control and strictly convex in the stock, those authors show that there are only two qualitatively different types of optimal paths, depending on whether the rate of growth of the resource is higher or lower than the discount rate.…”

Section: Introductionmentioning

confidence: 99%

The structure of optimal solutions for harvesting a renewable resource

Upmann

Gromov

2022

Natural Resource Modeling

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We consider the problem of optimal harvesting of a renewable resource whose dynamics are governed by logistic growth and whose payoff is proportional to the harvest. We consider both the case of a finite and an infinite time horizon and analyse the structure of the optimal solutions and their dependence on the parameters of the model. We show that the optimal policy can only have one of three structures: (1) maximal harvesting effort until the resource is depleted, (2) zero harvesting during an initial time interval followed by a subsequent switch to maximal harvesting effort, or (3) a singular solution, which corresponds to an intermediate level of harvesting, accompanied by the most rapid approach path. All three scenarios emerge, with minor variations, with finite and infinite time horizons, depending on the particular combination of parameters of the system. We characterize the conditions under which the singular solution is optimal and present suggestions for designing an optimal and sustainable harvesting strategy. Recommendations for Resource Managers: We have rigorously explored a standard optimal harvesting model and its steady states. We show that three different types of solutions may emerge: (i) maximal harvesting eventually leading to a complete depletion of the stock; (ii) maximal harvesting with a potential period of idleness leading to a positive stock; (iii) an initial phase of either no or full harvesting followed by a period of intermediate harvesting intensity leading to a positive stock (singular solution). With some modifications, similar results hold for a finite planning horizon. Which of these three scenarios emerges in the finite horizon case depends not only on the parameter values but also on the length of the planning horizon.

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“…These analyses aim at describing the structure of the optimal controls when the parameters of the model vary over some range. For example, Krasovskii and Tarasyev (2008) provide a qualitative analysis of the optimal solution of a general economic growth model (see also Bundău et al, 2009); LaTorre et al (2020) analyse the effects of different interventions in a simple macroeconomic epidemiological model, Baker et al (2019) analyse the structure of optimal management of invasive species, and Aseev et al (2005) study the optimal investments in an R&D model. Moreover, Aseev and Manzoor (2018) qualitatively characterize the solutions of an optimal harvesting problem with logistic growth: Assuming an effort-based consumption model where utility is strictly concave in the control and strictly convex in the stock, those authors show that there are only two qualitatively different types of optimal paths, depending on whether the rate of growth of the resource is higher or lower than the discount rate.…”

Section: Introductionmentioning

confidence: 99%