Course description

Mathematical biology is a wide subject area ranging from theoretical ecology, population dynamics and evolutionary dynamics to physiology, morphogenesis and reaction kinetics. The mathematical tools involved span ordinary and partial differential equations, difference equations, stochastic processes and individual-based models. This course will give an introduction to these topics simultaneously present how mathematical techniques can be used for understanding and interpreting biological phenomena. We will consider both simpler models that are analytically tractable and more complicated ones that are explored using simulations and other numerical techniques. 

Schedule

The course runs from March 25 - May 31, 2019.
Lectures are given on Tuesdays 10-12 and Thursdays 10-12 i
n MVL14, except for week 1 when both lectures are on Tue 26/3 10-12 and 13-15.

Teacher/Examiner

Philip Gerlee (gerlee@chalmers.se)

Content

Week 1: Populations dynamics
Week 2: Separation of time scales & oscillations
Week 3: Evolutionary game theory
Week 4: Adaptive dynamics
Week 5: Spatial models (Turing instability, Fisher eq.)
Week 6: Structured population models
Week 7,8: Student presentations 

Lecture Notes

Week 1: lecture 1, lecture 2
Week 2: lecture 1, lecture 2
Week 3: lecture 1, lecture 2
Week 4: lecture 1, lecture 2
Week 5: lecture 1, lecture 2
Week 6: lecture 1, lecture 2

Assignments

Week 1
Week 2
Week 3
Week 4

Week 5
Week 6


Relevant papers

Canonical equation
EGT in finite populations
Adaptive Dynamics
Turing pattern formation
Stage-structured model of chemotherapy
Size-structured model of metastasis


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