Learning outcomes

Mathematical models in tumor growth, population dynamics and wound healing.

Program

Cancer is the main cause of death in western societies, in spite of the constant
progress that has been made in therapy. In this course we will present mathematical
models of elementary processes arising commonly in population biology such as growth
(or more generally reactions), active movements (or more generally
transport-diffusion) of animals or cells for instance. We will focus particularly on
models for tumor growth and treatment and, if time permits, consider other topics
like wound healing and tissue regeneration or collective movements of bacteria
(including chemotaxis). These are all crucial subjects concerning not only
individuals but also public health policies. Competence in these issues is extremely
valuable for medical research and pharmaceutical companies.

We will start by considering ordinary differential equation models and then study
spatial ones (which involve partial differential equations). In tumor growth, we
will study cell birth and death, discuss the dynamics of cancer cells and in
particular the existence of quiescent and proliferative populations and how this
influences therapeutic strategies. Cytostatic drugs (which bloc cell proliferation),
cytotoxic drugs (which kill proliferative cells) and anti-angiogenetic ones (which
perturb the formation of new blood vessels to irrigate the tumor) act in very
different ways and we will see how the mathematical models show that it is essential
to combine different types of therapy to fight against cancer in a more efficient
way.. We will also discuss the issue of development of resistance to treatments and
of competition between healthy and tumor cells and even among different types of
tumor cells and how this can be used to keep tumors under control and prevent them
from coming very aggressive.

Examination Methods

oral presentation of a course topic