This course is an introduction to the most common mathematical models developed to solve biology and medicine problems. Deterministic and probabilistic models, and the main statistical approaches used to take into account the uncertainties that characterize complex biological systems will be discussed. At the end of the course students should be able to: - understand and critically discuss the main models of biological systems with particular reference to the validity of the assumptions and the definition of appropriate parameters; - develop and analyze simple models; - understand the effects of the parameters also in relation to the unavoidable uncertainty of their estimate; - compare the predictions of the models with the experimental data; - communicate the results in a multidisciplinary context
The entire course will be available online.
Part I (Albi)
- Single specie model: Malthus, Birth-Death, Logistic growth.
- Multi-species model: Predator-Prey, competition and cooperation.
- Epidemiological model: SIR, SEIR and age structured
- Time delay models
- PDE models of reaction and diffusion.
- Parameter identification for differential model
- Examples and exercises in class with dedicated softwares (Matlab and/or R)
Part II (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
- Biological oscillations
- statistical inference
- main statistical methods used in biomedicine with univariate and multivariate variables
- introduction to the R environment for scientific calculus and statistics
|M. Squassina, S. Zuccher||Introduzione all'Analisi Qualitativa delle Equazioni Differenziali Ordinarie. 332 pagine, 365 figure.||Apogeo Editore||2008||9788850310845|
|J. Murray||Mathematical Biology||Springer||2002||0-387-95223-3|
|J. D. Logan, W. R. Wolesensky||Mathematical Methods in Biology||2009||9780470525876|
|Brian Ingalls||Mathematical Modelling in Systems Biology: An Introduction|
Part A: written exam with the help of computer, solution of exercises on the basis of the one solved during the course. Students will be required to modify the numerical codes seen in Matlab/Octave/R. Possibility of midterm examination.
Part B: Oral evaluation. Students will be required to present a short essay on a bio-mathematical topic that they will choose by searching the scientific literature. Emphasis will be given to the students' ability to analyze and critically revise the selected problem. Students will be also required to reproduce and eventually extend all the mathematical aspects using the software MatLab or R.
The assessment methods could change according to the academic rules.