2016/12/14 by Camille Pouchol, Jean Clairambault, Pouchol, Camille +5
Mathematics · Medicine · #FOS: Mathematics #Liver physiology and pathology #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1612.04698
openalex publication_date 2016/12/14 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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.