Introduction to Mathematical Biology, spring 2011

This intermediate-level course is intended as a first introduction to mathematical biology. Subject areas include the dynamics of populations and of interacting species, ecosystem modelling, the dynamics of infectious diseases, natural selection and evolution. The participants will get acquainted with constructing and analysing mathematical models, mostly in form of continuous- and discrete-time dynamical systems. Mathematical biology is an active field of applied mathematics also at our Department, and interested students can continue with a number of advanced courses as well as start active research on undergraduate (BSc, MSc) and graduate level.

Lecturer

Eva Kisdi

Scope

10 cu.

Type

intermediate studies

Prerequisites

differential equations, elements of matrix algebra

Lectures

Weeks 3-9 and 11-18, Monday 10-12 and Friday 10-12 in room B321

Week 11: no lectures/no exercise class for Yuri Kuznetsov's course

Easter holiday

Exams and projects

Exam: 23 May (Monday) 10.15 - 13, in room B321 (lecture room)
 SECOND EXAM: 13 June (Monday) 10.15-13, in room B321 (lecture room)

Credits are awarded upon either a written exam or project work; the latter option is open to participants with sufficient activity in exercise classes. Problems for project work are described in this pdf file. Each participant must have a different project so problems are available on a first-come-first-served basis: When you have chosen a problem, email me with your choice.

Problem #6 (prey-predator-pathogen dynamics) is taken.
 Problem #9 (cell cycle) is taken.

Bibliography

N. F. Britton: Essential Mathematical Biology, Springer Verlag, Chapters 1-4
 L. Edelstein-Keshet: Mathematical Models in Biology, Birkhäuser, Chapters 1-6
 J. D. Murray: Mathematical Biology. I: An Introduction. Springer Verlag, Chapters 1-3, 10
 J. Hofbauer & K. Sigmund: Evolutionary games and population dynamics. Cambridge University Press, 1998.

Registration

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Feedback

You will receive an email from the WebOodi system that invites you to evaluate the course anonymously. Please do so: your feedback is very valuable for developing this course!

Exercise groups

Single exercise group Friday 12-14, in room B321, instructor Elina Roto
 Start at 12:30 (to have a lunch break)

Exercises (solutions by E. Roto)

Exercises 1.1 - 1.5  (28 January) solutions
Exercises 2.1 - 2.5  (4 February) solutions
Exercises 3.1 - 3.5  (11 February) solutions
Exercises 4.1 - 4.5  (18 February) solutions; bifurcation diagram of the Ricker model and the Matlab code to produce it
Exercises 5.1 - 5.5  (25 February) solutions
Exercises 6.1 - 6.5  (4 March) solutions
Exercises 7.1 - 7.5  (25 March) solutions
Exercises 8.1 - 8.5  (1 April) solutions
Exercises 9.1 - 9.4  (8 April) solutions
Exercises 10.1 - 10.5  (15 April) solutions
Exercises 11.1 - 11.4  (29 April) solutions
Exercises 12.1 - 12.5  (6 April, exercise class 10.15 am!) 

Figures

Survival data of the cohort of Finnish men born in 1900
 The quadratic map: figures in pdf; download the Excel file to play with
Lotka-Volterra competition
Simulated evolutionary tree
Survival Kit to Genetics
Speciation lecture

Follow-up

Biomathematics Day (11 May): free registration by email to jaakko.toivonen<funny character>helsinki.fi
 Welcome to (any of) the regular biomathematics seminars: http://mathstat.helsinki.fi/research/biomath/ -> seminars

Biomathematics courses: http://mathstat.helsinki.fi/research/biomath/ -> Teaching