Mathematical biology

• Program numerical solutions of ordinary differential equations occurring in mathematical biology.
• Develop and discuss differential equation models occurring in mathematical biology.
• Use general arguments to assess parameters values e.g. for the size and variability of fertility, mortality, and migration in populations
• Assess characteristic levels and time scales in population dynamic models.
• Determine which model structure is appropriate to answer a given question related to, e.g., resource management, risk assessment, or evaluation of SDGs.
• Utilize population models to answer such questions.
• Present and discuss a mathematical model for an audience of peers orally.
• Present a mathematical model in a presentation and poster.

The course introduces mathematical modeling of population dynamics of living organisms, from bacteria to whales. Focus is on conceptual models based on differential equations that illustrate basic concepts in population modelling. The overarching goal is to construct new mathematical models of a concrete biological reality, based upon existing simple models. In this manner the course both introduces to the technique of developing your own models; this skill is general and not specific for biological systems. The main topics are: single-species population models (logistic growth and structured populations). Models of interacting populations (competition and predator-prey relations). Functional responses. Somatic growth modelling. Exploitation of living systems. Seasonal succession. Epidemiological models. Spatial dynamics. Throughout, there is emphasis on developing presentation skills of mathematical models. At the end of the course the students develop their own project which will be evaluated by a poster session.

Course Literature
Karline Soetaert and Peter M.J. Herman: A practical guide to ecological modelling (freely available for DTU students).

• 36 – 49 (Thurs 13-17)

01035/01005, Basic knowledge of ordinary differential equations and linear algebra, corresponding to courses 01035/01005, or similar. Knowledge of Python, R, or Matlab programming. Those lacking those skills should follow 25328, which is the same course with added introduction to the required math and programming. No prior biological knowledge is required.

Short lectures and longer numerical (computer) exercises. The results of the exercises are presented by the students and discussed in plenum.

This course provides students with competences relevant to evaluate UN SDGs, particularly #14 (Life below water)