The course is an introduction to the basic and most known mathematical models developed to solve biological and medical problems.
We will discuss deterministic as well as probabilistic models, together with the statistical tools used to quantify the uncertainties characterizing complex biological systems.
At the end of the course the students should be able to :
- understand and discuss the main models of biological systems, with particular attention to the validity of the assumptions, and the definition of different parameters;
- develop and analyze simple models;
- understand the impact of the parameter, also with respect to their measure uncertainty;
- compare the predictions of the models with the experimental data;
- communicate the results in an interdisciplinary environment.
Part I (Albi)
A) Discrete, and continuous models:
* Single specie model: Mathus, Birth-Death, Logistic growth.
* Multi-species model: Predator-Prey, SIS, SIR, tumoral growth.
* Time delay models, ingle perturbed systems & oscillators.
* Models with noise.
B) Parameter identification and data analysis
* Statistical inference, theory of the estimators, maximum likelihood, test of hypothesis.
* Data fitting, Linear and non-linear regression, parameter identification.
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
|N. F. Britton||Essential Mathematical Biology||Springer||2003||978-1-4471-0049-2|
|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|
|Brian Ingalls||Mathematical Modelling in Systems Biology: An Introduction|
|V. Comincioli||METODI NUMERICI E STATISTICI PER LE SCIENZE APPLICATE||Universitá degli Studi di Pavia||2004|
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. The students will have to prepare and critically discuss a short essay.