**Aim**

The aim of the course is to introduce students to mathematical modeling of biological systems. The emphasis of this course is on macroscopic phenomena such as population growth, morphogenesis, and ecological problems. The modeling and computer-simulation techniques discussed are essential tools for understanding ecosystems, with applications, for example, to bioconservation. Microscopic phenomena, on the molecular level, are the subject of Computational Biology B (FFR 115).

**Learning outcome (after completion of this course, the student should be able to)**- Explain what can be, and what cannot be expected of mathematical models of biological systems

- Decide whether deterministic or stochastic models are required in a given context

- Efficiently simulate deterministic and stochastic models for population dynamics on a computer, understand and describe the implications of the results

- Perform linear stability analysis, and understand its limitations

- Efficiently simulate the partial differential equations describing advection-reaction-diffusion systems on a computer

- Apply non-linear time-series analysis to real data

- Understand the purpose and predictive power of models of evolution

- Write well-structured technical reports in English presenting and explaining analytical calculations and numerical results

- Communicate results and conclusions in a clear and logical fashion

**Content**

- Deterministic population dynamics: growth models, delay models, linear stability analysis, ecological implications

- nteracting species: Lotka-Volterra systems, phase-plane analysis, realistic predator-prey models

- Enzyme reaction kinetics: Michaelis-Menthen approximation, autocatalysis

- Pattern formation: Belousov-Zhabotinsky reaction, qualitative dynamics of relaxation oscillators, deterministic & stochastic approaches, reaction diffusion systems, traveling waves, spiral waves, morphogenesis

- Time-series analysis: noise in deterministic systems, linear time-series analysis, non-linear time-series analysis

- Evolutionary models

**Grades**

The grades are Fail (U), Pass (G) and Excellent (VG)**Examination**The examination is based on exercises and homework assignments (100%). The examinator must be informed within a week after the course starts if a student would like to receive ECTS grades.