Asymptotic analysis and optimal control of an integro-differential system modelling healthy and cancer cells exposed to chemotherapy
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2017-10-27Online Publication Date
2017-10-27Print Publication Date
2018-08Permanent link to this record
http://hdl.handle.net/10754/625960
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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 BVarXiv
1612.04698Additional Links
http://www.sciencedirect.com/science/article/pii/S0021782417301587ae974a485f413a2113503eed53cd6c53
10.1016/j.matpur.2017.10.007