Cancer chemotherapy optimization under evolving drug resistance

In the paper we are concerned with bilinear, infinite dimensional model of the evolution of drug resistance resulting from gene amplification. After p resenting biological background which justifies the mathematical model, som e of the model properties axe shown. Afterwards, a basic concept of transfo rming the system description into an integro-differential one is introduced . Next, a control theoretic approach to design a chemotherapy protocol is d iscussed. To achieve this, an optimization problem is formulated and the ne cessary conditions for optimal control are given. Basing on these condition s, gradient-based solution is proposed and tested numerically. Analysis of obtained numerical results suggests that, at least in some applications, su boptimal periodical control would be preferable as far as dynamical behavio ur of the model is concerned. In the final section, conclusions are drawn c oncerning the importance and applicability of the solution.