Mathematical Challenges in the Analysis of Continuum Models for Cancer Growth, Evolution and Therapy (18w5115)

Arriving in Oaxaca, Mexico Sunday, November 25 and departing Friday November 30, 2018


(INRIA Paris-Rocquencourt & Lab Jacques-Louis Lions, UPMC, Paris)

(University of Alberta)

Tomás Alarcón (Centre de Recerca Matemàtica, Bellaterra)


In the past five years or so, cancer modelling has been approached by innovative mathematical methods of continuous dynamical systems, structured in spatial and in phenotypical variables, representing heterogeneous populations of cells. Stimulated by unexpected failures of medical treatments (in particular due to drug-induced drug resistance) that most often consider targets at the single cell level, these recent methods take tumour dynamics at the cell population level into account, which is the most relevant level to tackle questions about tumour growth. Such models of tumour dynamics address problems arising from intra-tumour spatial and phenotypical heterogeneity, from tumour-stroma symbiosis and from evolutionary mechanisms used by the tumour cell population to escape therapeutic control. \\

These models take the form of systems of non-linear and non-local partial differential equations (PDEs) and the asymptotic analysis of such models raises numerous mathematical questions. Some of these questions have been solved, leaving however many other questions open. Most often, numerical simulations are used to get a rough understanding of what the solutions may look like. Research on these complex mathematical models is very active and theorems have been obtained in simplified settings. \\

Furthermore, methods of optimisation and optimal control applied to continuous models for targets representing pharmacological or radiological effects on healthy and tumour proliferation are also under development. There is an opportunity to find optimal controls in well-defined settings of tumour growth and treatment.\\

The objectives of this workshop are thus to confront new methods of mathematical modelling and optimal control with the most recent conceptions about evolution and cancer, to design new theoretical therapeutic strategies, aiming at reducing cancer to a mild, chronic disease.\\ We will structure the proposed 5-day workshop according to dedicated work groups and interventions of both outstanding international speakers and younger promising researchers following five main themes.