Simons Semester on Mathematical Biology School

The main theme of the school is the mathematical analysis of individual and structured models of population dynamics.

Leading international experts working on various aspects of mathematical biology will give introductory lectures and present state-of-art in their fields. We would also like to attract young people to this area of research.

In modern biology preliminary description of a population begins from individual-based models (IBMs), also called agent-based or microscopic models, which introduce local interactions between the members of a population, as mating and competition, and their influence on features or location of individuals. They can be also used for numerical simulations to show the global consequence of such interactions. By increasing the number of individuals to infinity and proper rescaling parameters we usually obtain a structured population models (SPMs), also called macroscopic description, which characterize the distribution of variables corresponding to properties of individuals as age, size, phenotypic traits and location in the space. A macroscopic model can be both deterministic and given by a transport equation (usually a partial differential equation with some nonlocal perturbation) or stochastic one (e.g. a stochastic process with values in the space of measures or a stochastic differential equation). Our aim is to study the transition from IBMs to SPMs as well properties of both types of models.