General course objectives
The course is an introduction to mathematical modelling of biological systems. It will enable the student to evaluate, develop and apply simple dynamical population models.
The course introduces mathematical modeling of population dynamics of living organisms, from virus to whales. Focus is on conceptual models based on differential equations that illustrates basic concepts in population and epidemiological modelling. An important aspect of the course is to develop an understanding of the biological assumptions underlying the models and on the ecological consequences of their results and develop the ability to connect an abstract mathematical model with a concrete biological reality. The main topics are: single-species population models (logistic growth). Epidemiological models (SIR models). Multi-species models (competition and predator-prey relations). Functional responses. Reaction kinetics and spatial population dynamics. Exploitation of living systems. Seasonal succession. Evolutionary models. Spatial dynamics. Some emphasis will be put on the development and evaluation of the presentation skills of the students. At the end of the course the students develop their own project which will be evaluated by a poster session.
01035/01005 , Basic knowledge of ordinary differential equations and linear algebra, corresponding to courses 01035/01005, or similar. Knowledge of matlab programming. Those lacking those skills should follow 25314, which is the same course with added introduction to the required math and programming. No prior biological knowledge is required.
A student who has met the objectives of the course will be able to:
- Present and discuss a mathematical model for an audience of peers.
- Program numerical solutions of ODE's occuring in mathematical biology.
- Develop and discuss differential equation models occurring in mathematical biology.
- Using general arguments to assess the size and variability of fertility, mortality, and migration in real populations, and their importance in models.
- Assess characteristic levels and time scales in population dynamic models.
- Argue for choice of parameter values in a model applied in a specific biological context.
- Determine the stability of steady states, and identify bifurcations.
- Determine which model structure is appropriate to answer a given question related to e.g. resource management or risk assessment.
- Utilize population models to answer such questions.