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

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    Type
    Article
    Authors
    Pouchol, Camille
    Clairambault, Jean
    Lorz, Alexander
    Trélat, Emmanuel
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2017-10-27
    Online Publication Date
    2017-10-27
    Print Publication Date
    2018-08
    Permanent link to this record
    http://hdl.handle.net/10754/625960
    
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    Abstract
    We consider a system of two coupled integro-differential equations modelling populations of healthy and cancer cells under chemotherapy. 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 cell 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.
    Citation
    Pouchol C, Clairambault J, Lorz A, Trélat E (2017) Asymptotic analysis and optimal control of an integro-differential system modelling healthy and cancer cells exposed to chemotherapy. Journal de Mathématiques Pures et Appliquées. Available: http://dx.doi.org/10.1016/j.matpur.2017.10.007.
    Publisher
    Elsevier BV
    Journal
    Journal de Mathématiques Pures et Appliquées
    DOI
    10.1016/j.matpur.2017.10.007
    arXiv
    1612.04698
    Additional Links
    http://www.sciencedirect.com/science/article/pii/S0021782417301587
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.matpur.2017.10.007
    Scopus Count
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    Articles; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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