Mathematical models in biology
Scientific Disciplinary Sector (SSD)
MAT/05 - MATHEMATICAL ANALYSIS
II sem. dal Mar 1, 2017 al Jun 9, 2017.
This course is an introduction to the most common mathematical models in biology and biomedicine. At the end of the course the students should be able to:
- understand and critically discuss basic models of biological systems, with particular emphasis to the validity of assumptions and of model parameters;
- model simple phenomena, analyze them (numerically and/or analytically), and understand the effect of parameters;
- compare the predictions given by the models with experimental data;
- communicate results in interdisciplinary teams
Part A - dott. Simone Zuccher
Different mathematical models in biology will be presented. They are divided into discrete and continuous ones each of which can be further divided into scalar or vectorial. Theoretical results will be recalled (not proved because already known from previous courses in Mathematical Analysis and Dynamical Systems) and then applied to the study of the different models.
- The discrete, scalar case. Malthusian growth and quadratic logistic model. Discussion of bifurcation depending on a parameter, p-cycle and its stability, bifurcation diagram, route to chaos.
- The discrete, vectorial case. Two-species discrete models: host-parasite, prey-predator and inter-action between species.
- The continuous scalar case. Growth of bacteria (continuous logistic map), exact solution. Qualitative study of ordinary differential equations.
- The linear planar case. The T-D plane, examples.
- The non-linear continuous planar case. The spread of disease model, the Lotka-Volterra model.
Course notes are available at http://profs.sci.univr.it/~zuccher/teaching/
Part B - dott. Roberto Chignola
- probabilistic models for biomedicine
- the Luria and Delbrück experiment
- growth models for population biology
- allometry and scaling laws
- phenomenological models for tumor growth
- models for cell physiology
- multi-scale models in oncology
Course notes are available at: http://profs.sci.univr.it/~chignola/teaching.html
Part A: The exams is an oral interview. Students will be asked to discuss the contents presented during the course Part A and to provide the solution in Matlab/Octave to the exercises assigned during the course.
Part B: Oral evaluation. The students will have to prepare and critically discuss a short essay.