Unexistence of limit cycle in an optimal control problem of a population of diabetics

Abstract : This paper deals with one of the most important public health problem in the whole world that is diabetes, and more precisely its complications. From a model examining the complications or not of a population of diabetics , we associate a nonlinear optimal control problem. Considering the previous, we prove that the equilibrium state exists and is a saddle point. Moreover, we claim the unexistence of limit cycle in such a population, which is an interesting result concerning this world evil. Then we give some examples for which we characterize the equilibrium state which is not necessarily admissible.
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Submitted on : Wednesday, August 15, 2018 - 4:23:37 PM
Last modification on : Thursday, August 16, 2018 - 5:30:02 PM

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Séverine Bernard, Ténissia César, Silvère Paul Nuiro, Alain Piétrus. Unexistence of limit cycle in an optimal control problem of a population of diabetics . Revista de Matematica: Teoria y Aplicaciones , 2018, 25 (2), pp.239-259. 〈10.15517/rmta.v25i2.33692〉. 〈hal-01857368〉

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