Teaching code

4S004794

Academic staff

Giacomo Albi, Roberto Chignola

Coordinatore

Giacomo Albi

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

BIO/13 - EXPERIMENTAL BIOLOGY

Period

Semester 1 dal Oct 3, 2022 al Jan 27, 2023.

Lessons timetable Moodle Seminars

Learning objectives

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

Prerequisites and basic notions

Differential calculus, foundations of dynamical systems, and linear algebra. Computer use and programming language (mainly MATLAB / OCTAVE)

Program

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

Bibliography

Didactic methods

Part I: this part will be taught through lectures
Part II: this part will be taught through lectures

The rights of students will be preserved in situations of travel limitation or confinement due to national provisions to combat COVID or in particular situations of fragile health. In these cases, you are invited to contact the teacher directly to organize the most appropriate remedial strategies.

Learning assessment procedures

Part I: 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 II: 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.

Evaluation criteria

Part I: Students will have to demonstrate that they can correctly solve exercises similar to those seen in class, to be able to formulate simple mathematical and statistical models starting from biological data.
Part II: 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.

Criteria for the composition of the final grade

Arithmetic average of the written grade on Part I and of the oral grade on Part II

Exam language

Italiano