Introduction to Mathematical Methods in Population Theory

Jacek Banasiak was born on 15th March 1959 in Łódź, Poland. The current holder of the DSI/NRF SARChI Chair in Mathematical Models and Methods in Biosciences and Bioengineering at the University of Pretoria, he is also a research professor at the Łódź University of Technology in Poland and a visiting professor at the University of Strathclyde in Glasgow, Scotland. His research interests are nonlocal integro-differential models in kinetic theory, mathematical biology and fragmentation-coagulation theory, asymptotic analysis of multiple scale problems and epidemiological modelling. Up to this point in his career, he has authored/co-authored seven research monographs and over 145 refereed research papers. He is a recipient of the South African Mathematical Society Award for Research Distinction (2012), Cross of Merit (Silver) of the Republic of Poland (2013), 1st prize for the best paper in applied mathematics from the Centre for Applications of Mathematics of Gdańsk (2014), as well as the Minister of Science and Education of the Republic of Poland Award for Scientific Achievements in 2022. He is the Editor-in-Chief of Afrika Matematika (Springer journal) and a member of editorial boards of several other journals.

• 1 Mathematical modelling.- Part I Unstructured Models.- 2 Models with discrete time.- 3 Models with continuous time.- 4 Qualitative theory for a single equation.- Part II Models with discrete structure.- 5 Linear models with discrete structure.- 6 Continuous time non-linear models for interacting species and age-structured populations.- 7 Discrete time non-linear models for interacting species and structured populations.- 8 Positivity in natural science models.- Part III Models with continuous age structure.- 9 McKendrick–von Foerster model.- 10 Basic nonlinear models. Part IV Appendices.- A Spaces, norms and order.- B Differential equations and systems.- C Linear algebra tools.- D First order partial differential equations and the method of characteristics.