Course content:

In this module, we will develop simple models of biological phenomena from basic principles. We will introduce analysis techniques to investigate model dynamics in order to deduce biologically significant results. We will use (systems of) ordinary differential equations, difference equations, and partial differential equations to study population dynamics, biochemical kinetics, epidemiological dynamics, evolution, and spatiotemporal phenomena. Throughout, we will discuss the biological implications of our results.

Aims:

Introduction to the fundamentals of Mathematical Biology.

Objectives:

• To develop simple models of biological phenomena from basic principles
• To analyse simple models of biological phenomena using mathematics to deduce biologically significant results
• To reproduce models and fundamental results for a range of biological systems
• To have a basic understanding of the biology of the biological systems introduced

Books:

H. Van den Berg, Mathematical Models of Biological Systems, Oxford Biology, 2011
James D. Murray, Mathematical Biology: I. An Introduction. Springer 2007
Keeling, M.J. and Rohani, P. Modeling Infectious Diseases in Humans and Animals, Princeton University Press, 2007
Anderson, R. and May, R. Infectious Diseases of Humans, Oxford University Press, 1992

Outline syllabus for publication

• Mean-field Population dynamics a. Single-species population models, b. Multi-species population models
• Models of biochemical kinetics
• Epidemiological models
• Models of evolution and game theory models
• Spatio-temporal models of population dynamics a. Travelling waves, b. Pattern formation

 Reading list

• H. van den Berg, Mathematical Models of Biological Systems, Oxford Biology, 2011
• James D. Murray, Mathematical Biology: I. An Introduction Springer 2007
• Anderson, R. and May, R. Infectious Diseases of Humans, Oxford University Press, 1992
• Keeling, M.J. and Rohani, P. Modeling Infectious Diseases in Humans and Animals, Princeton University Press, 2007