PROGRAM

SEAMS School - Mathematical Modelling in Biology

Hanoi, March 8-15, 2017

Course M1: Mathematical Modeling Techniques for Biological Systems

Lecturer: Hien Tran

Abstract: This course seeks to provide students with a fundamental understanding of how mathematics and statistics are applied to problems in life sciences. Our approach will be through several “case studies” problems that arise in biological applications. For each case study we will discuss why a model is needed and what goals are to be sought. We will examine the mathematical models both analytically and computationally in order to compare their behavior with that exhibited by the modeled phenomena. Such a comparison can be achieved quantitatively through model verification and validation, which are central to the process of model development and evaluation for all complex systems. Some computational tools are also presented to simulate the models.

Course M2: Branching Processes

Lecturer: Marc Peigne

Abstract: Galton-Watson branching processes describe the evolution of a population, assuming that individuals reproduce independently of each other to some given offspring distribution. One of the most important question concerns the probability of extinction of the population, with some transition phenomenon from subcriticality to supercriticality in several steps. We will present well known results in two natural generalizations and also recent ones concerning multi-type Galton-Watson processes in random environment. These results rely on a stimulating interplay between branching process theory and random walk theory.

Course M3: Octave

Lecturer: Thanh Ha Do

Abstract: The course will provide an introduction to computing using Octave, the free software. It will teach you how to perform advanced data analysis, solve common numerical linear algebra problems, and simulate the mathematical models for biological systems related to the materials presented in course M1 of Professor Hien Tran.

Course M4: An introduction to mathematical population genetics

Lecturer: Tat Dat Tran

Abstract: This course seeks to provide students Mathematical models: Wright-Fisher models, Wright-Fisher models with other evolutionary factors (mutations, selection, recombination, migration), Fleming-Viot models.

• A fundamental knowledge about mathematical population genetics;
• Some advanced methods in studying mathematical population genetics;
• Open problems in mathematical population genetics.

Course M5: Individual-based modeling of population dynamics

Lecturer: Fugo Takasu

Abstract: Models of population dynamics have been usually described by ordinary or partial differential equations. These models describe dynamics of population size or distribution over space as continuous variable at the expense of biological realism of being individual. Individual-based models assume individuals as "base unit", and thus they are more realistic but at the cost of mathematical tractability; dynamics of population size or distribution over space becomes inherently stochastic and model analysis is not straightforward. The course content will be 1) Introduction of ODE/PDE models used in population ecology, 2) Reconstruction of these models as individual-based models, and 3) Mathematical analysis of these individual-based models.