This residential month is along the lines of former sessions organized at CIRM each February since 2001 by a group of Marseille researchers. In February 2020, the members of the Institute of Mathematics of Marseille involved in collaborations with biologists propose to gather researchers from around the world, at CIRM, around the theme of Mathematical Biology. The interplay between mathematics and biology has developed rapidly since the last decades of the 20th century, both in France and in all developed countries. Progress in biological science requires mathematical modeling, while the increased quantity of available data makes it possible to compare models with reality, and requires a lot of statistics. This is true at all levels of life. The evolution of species, their interactions among themselves and with their environment, ecology and the condition for maintenance of biodiversity are major fields where biologists, mathematicians and statisticians interact. Furthermore, emerging epidemics (such as AIDS, H1N1, EBOLA, etc.) and the development of antibiotic resistance call for progress in the mathematical modeling of epidemics, and in the interplay between their dynamics and the evolution of viruses.
While medicine has made huge progress in recent history, society requires better still treatments for cancer. Another challenge faced by medicine is to adapt each treatment to the specific characteristics of each patient. This requires mathematical modeling and statistics. Interaction networks are crucial in everyday life, and their size calls for mathematical modeling, while making it particularly challenging. Here, the high complexity behind any realistic model for biology is particularly obvious. In all areas of mathematical biology, a simplified model is the first step, and, like in physics, the simplest, very idealized models are often the most useful. However, the high complexity of realistic models makes it necessary to combine various mathematical tools. Those who want to make significant contributions to mathematical biology should be ready to use a big variety of mathematical techniques, ranging from analysis (in particular ODEs and PDEs), to probability and stochastic processes, not to mention statistics. However, many younger colleagues are trained in only one of those three fields. This is why this thematic month will start off with a research school on ODEs, PDEs, Probability and Statistics. A minimal knowledge of those areas of applied mathematics is recommended for any mathematician wanting to work at the interface with biology. The research school will be followed by three conferences gathering the ODE, PDE, Probability and Statistics communities. A final research school on networks will close this five-week event.