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IMA Journal of Mathematical Control and Information 2000 17(1):33-51; doi:10.1093/imamci/17.1.33
© 2000 by Institute of Mathematics and its Applications
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Therapy burden, drug resistance, and optimal treatment regimen for cancer chemotherapy

JOSÉ L. BOLDRINI{dagger} and MICHEL I. S. COSTA{ddagger}

Universidade Estadual de Campinas, Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computaç;ão Científica C.P. 6065, 13081–970, Campinas, SP, Brasil
Laboratório Nacional de Computação Científica - CNPq, Av Getúlio Vargas, 333, 25651–070, Petrópolis, Rio de Janeiro, Brasil

{dagger}Email: boldrini{at}ime.unicamp.br

{ddagger}Author to whom correspondence should be addressed. Email: michel{at}Incc.br

Three nonlinear models of tumour cell growth under continuous delivery of cycle nonspecific anticancer agents are studied. A dynamical optimization problem with the objective of minimizing the final level of tumour cells is posed for these mathematical setups. The simplest setup does not possess toxicity constraints, whereas the other setups contain a dynamical equation describing the therapy burden as a toxicity criterion. In addition, the third setting contains the dynamics of drug resistant cells. A discussion conceming the optimal strategies of the respective models is performed.

Keywords: drug resistance; therapy burden; optimal control.


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