<div class="tex2jax_process">The school aims to introduce students and young researchers to several important research directions in mathematical biology, with a focus on deterministic mathematical models used to describe complex biological processes. These models play a central role in understanding phenomena such as population dynamics, epidemiology, tumor growth, and respiratory system functioning.
Part of the program will focus on the mathematical modeling of biological populations using structured population dynamics and transport equations. Participants will be introduced to classical frameworks such as the McKendrick–Von Foerster models and renewal equations, which provide powerful tools for describing the evolution of populations structured by age, size, or other physiological characteristics. These approaches allow mathematicians to analyze key qualitative properties of biological systems, including stability, long-term behavior, and pattern formation.
Another component of the school will address epidemiological models based on the classical SIR (Susceptible–Infected–Removed) framework and its extensions. Participants will explore how these models describe the spread of diseases and how mathematical tools can be used to design optimal control strategies in applications such as plant epidemiology and crop protection.
The program will also present mathematical models used in oncology, ranging from simple systems of ordinary differential equations to more advanced approaches involving structured populations and mixture theory. These models help describe interactions between tumor cells and their microenvironment and analyze the effects of medical treatments.
In addition, the school will introduce aspects of fluid dynamics relevant to biological applications, including the analysis of the incompressible Navier–Stokes equations. Applications to biological flows, such as ventilation and gas diffusion in the lungs, will also be discussed.
Throughout the program, emphasis will be placed on the connection between theoretical analysis and practical applications. Participants will gain familiarity with modern mathematical tools used in the study of biological systems, including optimal control methods, asymptotic analysis, and numerical approaches. The school is designed for Master’s students, PhD students, and young researchers with a background in mathematics, and aims to provide them with both the theoretical foundations and the motivation to pursue research in this interdisciplinary field.
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