# MA4L1 Mathematical Modelling in Biology and Medicine

**Lecturer: **Markus Kirkilionis

**Term(s): **Term 1

**Status for Mathematics students: **List C

**Commitment: **30 Lectures

**Assessment: **Written examination (50%), Project work (50%)

**Prerequisites: **no formal requirements

**Leads To:**

**Content:**

**Part A Mathematical Modeling in the Life Sciences**

**Week 1:** **Mathematical Foundations (Repetition as warming up)**

Lecture 1 Introduction to graph theory, relevance for the Life Sciences, degree distributions and their characteristics, examples.

Lecture 2 Random variables and probability distributions, stochastic processes, examples.

Lecture 3 Statistics and data analysis

**Week 2:** Biochemical Reaction Systems and Rule Based Systems

Lecture 1 Introduction to reaction schemes.

Lecture 2 Hypergraphs and chemical complexes.

Lecture 3 Extended reaction schemes.

**Part B Applications.**

**Week 3: Morphogenesis, Cellular Transport Processes
**Lecture 1 Dynamical systems, semi-Flows and functional analysis.

Lecture 2 Reaction-diffusion equations and models of pattern formation/morphogenesis.

Lecture 3 Qualitative behaviour, more pattern formation, modeling transport and reaction.

**Week 4: Cell Biology and Cell Cultures
**Lecture 1 Modeling in Genetics.

Lecture 2 The Cell Nucleus.

Lecture 3 The Chemostat.

**Week 5: Cell Cultures and Physiology
**Lecture 1 Physiologically Structured Populations.

Lecture 2 The Cell Cycle.

Lecture 3. Structured Populations in the Chemostat.

**Week 6: Future Medicine
**Lecture 1 Learning Algorithms I.

Lecture 2 Learning Algorithms II.

Lecture 3. Data mining in medicine.

**Week 7: Future Medicine
**Lecture 1 Numerical simulation in medicine.

Lecture 2 Numerical simulation in medicine.

Lecture 3 Numerical simulation in medicine.

**Week 8: Global Ecology
**Lecture 1 Population Dynamics and Global Disturbances.

Lecture 2 Models of Biodiversity.

Lecture 3 The Growth of Cities and Landscape Patterns.

**Week 9: Evolutionary theory
**Lecture 1 Models of evolution.

Lecture 2 Examples of complex evolving systems, biology and language.

Lecture 3 Examples of complex evolving systems, game theory.

**Week 10: Climate Change and Feedback to Living Systems
**Lecture 1 The global climate and its modeling.

Lecture 2 The global climate and oceans.

Lecture 3 The global climate and vegetation.

**Aims:
**• Introduce the student to advanced mathematical modelling in the Life Sciences in a systematic way.

• Making the student aware how to choose and use different modelling techniques in different areas of the Life Sciences.

• A clarification about the mathematical content and structure of mathematical models in the Life Sciences.

• A general introduction to modern systems analysis tailored to the Life Sciences.

**Objectives:
**By the end of the module the student should be able to:

Orient in the latest research on Mathematical Biology

Apply methods learned in the module to new problems inside the scope of Mathematical Biology.

Quickly solve standard problems occurring in Mathematical Biology

**Books:
**Newman, M. 2010 Networks: an introduction. Oxford University Press.

Metz, J. A. J. and Diekmann, O. 1986. The dynamics of physiologically structured populations. Lecture Notes in Biomathematics. 68.

Keener, J. and Sneyd, J. 1998 Mathematical Physiology. Springer-Verlag.

Murray J.D. 2002. Mathematical Biology. New York: Springer.

Iannelli, M., Martcheva, M., and Milner, F. A. 2005 Gender-Structured Population Modeling: Mathematical Methods.