TY - JOUR
T1 - Asymptotic analysis and optimal control of an integro-differential system modelling healthy and cancer cells exposed to chemotherapy
AU - Pouchol, Camille
AU - Clairambault, Jean
AU - Lorz, Alexander
AU - Trélat, Emmanuel
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2017/10/27
Y1 - 2017/10/27
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/625960
UR - http://www.sciencedirect.com/science/article/pii/S0021782417301587
UR - http://www.scopus.com/inward/record.url?scp=85041901945&partnerID=8YFLogxK
U2 - 10.1016/j.matpur.2017.10.007
DO - 10.1016/j.matpur.2017.10.007
M3 - Article
SN - 0021-7824
VL - 116
SP - 268
EP - 308
JO - Journal de Mathématiques Pures et Appliquées
JF - Journal de Mathématiques Pures et Appliquées
ER -