Mini-course 1: Prof Stephanie Portet

Course title: Mathematical Modelling as an Investigation Tool 
Description: Mathematical modelling has become an indispensable tool for investigating complex biological systems, formalizing hypotheses, and making quantitative predictions. This four-part lecture series provides an accessible introduction to the foundational concepts of mathematical biology by guiding attendees through the complete modelling cycle. We will begin by discussing the standard modelling workflow and basic concepts, followed by the practical steps of translating biological mechanisms into mathematical equations. We will then explore the mathematical analysis of Ordinary Differential Equation (ODE) models to understand and predict system dynamics. Finally, the series will cover how to bridge the gap between theory and observation by linking models to empirical data through model calibration and selection. Throughout the lectures, theoretical and methodological concepts will be illustrated using concrete, real-world examples drawn from ecology, epidemiology, and cellular and molecular biology.

• Lecture 1: Introduction to Mathematical Modelling - Workflow and Basic Concepts
• Lecture 2: Writing a Model
• Lecture 3: Mathematical Analysis of ODE Models
• Lecture 4: Model Calibration and Selection

Mini-course 2: Prof Sophie Dabo

Course title: Introduction to Statistical and Machine Learning
Description: This course offers an introduction to statistical and machine learning, integrating principles from classical estimation theory with contemporary approaches to predictive modeling. The curriculum systematically develops from mathematical statistical inference, including probability theory, properties of estimators, and parametric/non-parametric model fitting, toward fundamental supervised and unsupervised learning methodologies. By combining formal theoretical analysis with applied components, the course provides students with the conceptual and methodological framework necessary to interpret, assess, and implement learning algorithms in practical applications. Prior exposure to machine learning is not assumed; however, basic knowledge of probability and linear algebra is recommended.

• Lecture 1: From Statistical Modeling to Learning
• Lecture 2: Unsupervised Learning and Perspectives
• Lecture 3: Core Supervised Learning Methods
• Lecture 4: Core Supervised Learning Methods (cont)

Mini-course 3: Prof Julien Arino

Course title: Mathematical Modelling in Days of LLMs and genAI
Description: In January 2020, I published a paper titled “Mathematical epidemiology in a data-rich world”. It is interesting that this feels like an eternity ago: since then, we had a pandemic and LLMs emerged as transformational tools. In this course, I will explore how LLMs and genAI can be used in the modelling process, using mostly examples from epidemiology. I will focus on the use of tools that do not require a subscription and can be run on small machines.

• Lecture 1: Neural Networks, LLMs and genAI: a Brief Theoretical Overview
• Lecture 2: Neural Networks, LLMs and genAI: Computational Aspects
• Lecture 3: Some Case Studies (Part 1)
• Lecture 4: Some Case Studies (Part 2)

Mini-course 4: Prof James Watmough

Course title: Introduction to Mathematical Epidemiology and Immunology
Description: My main objective with this four-lecture sequence is to introduce some of the core concepts of epidemiological and immunological models. The first lecture starts with a few simple stochastic processes and ode models from population dynamics and subsequent lectures use these as a framework for the classic models for disease-transmission, viral dynamics, and immune dynamics. Throughout the lectures you will gain a better understanding of the processes behind the terms we see in classic models and give some meaning to parameters appearing in the models. This will help you in all stages of model design and analysis, as I will illustrate with a few simple case studies. In the interest of accessibility, the lectures focus on the construction and simulation of models and gloss over the underlying mathematical theories. No prior knowledge of stochastic processes is assumed, but some knowledge of probability theory is helpful.

• Lecture 1: Simple Stochastic Processes and Associated ODE Models
• Lecture 2: Core Concepts of Mathematical Epidemiology and Immunology
• Lecture 3: Immune System Dynamics, Waning Immunity, Maturation Delays
• Lecture 4: Modelling at Multiple Scales

Mini-course 5: Prof Mohammed Yiha Dawed 

Course title: Introduction to Mathematical Ecology and Analysis
Description: The aim of this mini course is to offer an introduction to mathematical ecology through the development and analysis of mathematical models in order to comprehend ecosystems. This course starts off with basics in ecology and uses of mathematics in ecology modeling and follows up with classical growth models in population which include the exponential, logistic, Gompertz, and theta-logistic models. Models of interacting species such as predator prey model, competition, and mutualism models are discussed next. Finally, the study of spatial ecology is included through the use of patch (meta population), reaction diffusion, and advection diffusion models.

• Lecture 1: Introduction to Mathematical Ecology  and Population Growth Models
• Lecture 2: Species Interactions and Spatial Ecology

Mini-course 6: Prof Legesse Lemecha Obsu

Course title: An Introduction to Optimal Control Theory and Its Applications in Public Health and Ecology
Description: Optimal control theory provides a mathematical framework for designing effective intervention strategies in dynamic systems under constraints. This lecture introduces the fundamental concepts and applications of optimal control, emphasizing biological systems in public health and ecology. Participants will explore the formulation of controlled ordinary differential equation models, including state and control variables, objective functionals, admissible controls, and system constraints. The analytical foundation will cover the Pontryagin Maximum Principle, Hamiltonian formulation, adjoint equations, transversality conditions, and optimality characterization. Numerical approaches, particularly the forward–backward sweep method, will be introduced to connect theoretical analysis with computational implementation. Applications will be explored through two major domains. In public health, participants will examine how optimal control models support decision-making in vaccination planning, treatment optimization, isolation strategies, and resource allocation for infectious disease control. In ecology, the lecture will demonstrate applications in pest management, biodiversity conservation, and sustainable ecosystem management. The lecture concludes with emerging research directions such as stochastic and optimal control under uncertainty, and data-driven approaches that integrate machine learning with mathematical optimization.

• Lecture 1: Foundations of Optimal Control Theory and Basic Concepts
• Lecture 2: Computational Method and Applications in Public Health and Ecology

Mini-course 7: Prof Patrick M Tchepmo Djomegni

Course title: Structured Models in Biology
Description: This course introduces the theory and applications of structured partial differential equation (PDE) models in biomathematics, with particular emphasis on age- and size-structured population dynamics. It begins by motivating the need for structured population models and examining the limitations of classical ordinary differential equation (ODE) models in representing biological heterogeneity arising from variations in physiological characteristics such as age, body size, developmental stage, infection age, and spatial location. The course then reviews the fundamental mathematical concepts that underpin structured population modelling, including conservation laws, transport equations, and the formulation of initial and boundary conditions. Building upon these foundations, we derive structured PDE models from first principles, formulate appropriate boundary conditions, and investigate their applications in cell population dynamics, tumor growth, epidemiology, and ecological population dynamics.

• Lecture 1: Introduction, motivating applications, derivation of McKendrick–von Foerster equation
• Lecture 2: Transport Equation on R and R+ (Part 1)
• Lecture 3: Transport Equation on R and R+ (Part 1)
• Lecture 4: Formulation and Analysis of Structured PDE Models Arising in Epidemiology and Oncology