Asymptotic analysis and optimal control of an integro-differential system modelling healthy and cancer cells exposed to chemotherapy - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal de Mathématiques Pures et Appliquées Year : 2018

Asymptotic analysis and optimal control of an integro-differential system modelling healthy and cancer cells exposed to chemotherapy

Abstract

We consider a system of two coupled integro-differential equations modelling populations of healthy and cancer cells under therapy. Both populations are structured by a phenotypic variable, representing their level of resistance to the treatment. We analyse the asymptotic behaviour of the model under constant infusion of drugs. By designing an appropriate Lyapunov function, we prove that both densities converge to Dirac masses. We then define an optimal control problem, by considering all possible infusion protocols and minimising the number of cancer cells over a prescribed time frame. We provide a quasi-optimal strategy and prove that it solves this problem for large final times. For this modelling framework, we illustrate our results with numerical simulations, and compare our optimal strategy with periodic treatment schedules.
Fichier principal
Vignette du fichier
ArticleControlCancer_v1_HAL.pdf (814.4 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-01416594 , version 1 (14-12-2016)

Identifiers

Cite

Camille Pouchol, Jean Clairambault, Alexander Lorz, Emmanuel Trélat. Asymptotic analysis and optimal control of an integro-differential system modelling healthy and cancer cells exposed to chemotherapy. Journal de Mathématiques Pures et Appliquées, 2018, 116 (9), pp.268-308. ⟨10.1016/j.matpur.2017.10.007⟩. ⟨hal-01416594⟩
1086 View
377 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More