Mathematical Modelling Techniques

This book is based on lecture materials originally developed by Harald E. Krogstad for the MSc course Mathematical Modelling at the Norwegian University of Science and Technology (NTNU) and later adapted for the MASTMO MSc program at Hawassa University, Ethiopia. Following Prof. Krogstad’s passing in 2020, the project was continued by Mohammed Yiha Dawed and Patrick M. Tchepmo Djomegni, with contributions in mathematical epidemiology from Julien Arino. The text offers a structured and comprehensive introduction to mathematical modelling, blending classical methods with original content. Its goal is to equip beginning graduate students and advanced undergraduates in applied mathematics, statistics, and related fields with the tools to formulate, analyze, and interpret models across natural sciences, engineering, and biology.

What distinguishes this book is its balance of theory and application, bridging rigorous mathematics with practical modelling problems. Students learn both the conceptual foundations and computational approaches, preparing them to tackle real-world challenges.

Key Features Include:

Introduction to dimensional analysis, scaling, and perturbation methods
Equilibrium, bifurcation, and hysteresis analysis
Classical and generalized population and epidemic models, including logistic, Lotka-Volterra, and SIR models
Early introduction to partial differential equations through conservation-based modelling
Applications to road traffic, mechanics, diffusion, and small project-based exercises
Worked examples and chapter-end exercises for self-study.
Concise “first aid” guide for solving first-order quasi-linear PDEs.

This book is ideal for beginning graduate students and advanced undergraduates in applied mathematics, statistics, and related disciplines. Its combination of theory, applied examples, and project-based

Author Biography

Harald E. Krogstad was a distinguished Norwegian applied mathematician and Professor Emeritus at Norwegian University of Science and Technology, Trondheim, where he earned his PhD in 1969. He made seminal contributions to signal processing, ocean wave dynamics, and numerical simulations. Author of over 110 publications, his expertise spanned wave spectra, digital signal processing, and stochastic analysis.

Mohammed Yiha Dawed is an Associate Professor of Applied Mathematics at Hawassa University, Ethiopia, where he earned his PhD in 2017. He previously served as Head of the Department of Mathematics and contributed to Ethiopia’s national curriculum by editing Grade 9 and 10 textbooks and teachers’ guides. His research focuses on differential equations applied to epidemiology, ecology, and eco-epidemiology.

Patrick M. Tchepmo Djomegni is an Associate Professor at North-West University and a C2-rated researcher by South Africa’s NRF. He earned his PhD in Applied Mathematics from the University of KwaZulu-Natal in 2015. Founder of 3MC, he serves on CIMPA’s Governing Board and co-leads the CNRS-AFRICA JPR FANE-MATH-PE chair (2024-2027). His research centers on differential equations in epidemiology, ecology, and oncology.

Julien Arino is a Professor with the Department of Mathematics at the University of Manitoba, in Winnipeg, Canada. He obtained his PhD at INRIA Sophia Antipolis, France, in 2001. He is a mathematical biologist working mostly in epidemiology and ecology. He is particularly interested in the relationship between population movement and the spatio-temporal spread of infectious pathogens.