Reaction-Diffusion Equations Arising in the Mathematical Modelling of Population Dynamics - first part

During the last eighty years, reaction-diusion equations have been extensively used to achieve a better

understanding of a wide range of ecological phenomena. The goal of this mini course is to provide

a gentle introduction to reaction-diusion equations arising in the mathematical modelling of population

dynamics. In particular, the cases of space-structured populations and phenotype-structured

populations will be considered. The main qualitative properties of the solutions to these equations

will be studied and examples of possible real world applications will be discussed. The course will be

organised into two related parts as follows:

Part 1. Reaction-diusion equations for space-structured populations

1.1 Local reaction-diusion equations modelling space dispersal

1.2 Local reaction-diusion equations modelling spatial dynamics of invasion

1.3 Local reaction-diusion equations modelling competitive interactions

Part 2. Phenotype-structured models for tumour growth

2.1 Simple models for tumour growth

2.2 Mathematical models for natural selection

2.3 Mathematical models for mutation-selection dynamics

Recommended Books

 J.D. Murray

Mathematical Biology I: An Introduction

 Springer, 3rd ed. 2003

J.D. Murray

Mathematical Biology II: Spatial Models and Biomedical Applications

 Springer, 3rd ed. 2003

B. Perthame

Transport Equations in Biology

 Birkhauser, 2007

B. Perthame

Parabolic Equations in Biology - Growth, Reaction, Movement and Diusion

 Springer, 2015