The course aims at giving the students the knowledge relative to the development of mathematical and statistical models applied to biology and medicine. The proposed methods will be analyzed from both a qualitative and a quantitative point of view. Statistical tools to validate and fit modeling outcomes to experimental data will be introduced as well. A part of the course will be focused on the study of methods to analyze genomic data obtained by  DNA and RNA sequencing techniques.


By the end of the course students will have gained (i) the basic knowledge of different biological and biomedical phenomena; (ii) the knowledge of several types of mathematical and statistical models used to simulate the described phenomena; (iii) the ability to construct and evaluate the proposed mathematical and statistical models; (iv) the knowhow to adapt and fit theoretical methods to both experimental and predictive data; (v) the knowhow to analyze the obtained models with analytical, statistical and numerical techniques.

A good knowledge of mathematical and statistical concepts, tools, and methods introduced in previous courses. Particular attention has to be paid to: -differential and integral calculus; -complex analysis; -Markov chains; -elementary probability theory; -methods of inferential, frequency, and Bayesian statistics.

The course will tackle the following topics: 1) general concepts of deterministic (bio)-chemical pathways: positive and negative feedback loops. Mutually inhibitory feedback loops; 2) population dynamics. SIR (and SIR-based) models. Models for growth of cell aggregates in physio-pathological situations. Analysis of exponential, Gompertz, and logistic growth laws; 3) bi- and three-compartmental models for pharmacokinetics and pharmacodynamics; 4) stochastic models of chemical reactions. Bayesian approaches for the estimate of the parameters of the models introduced in 2) and 3); 5) clinical trials, randomization, sequential clinical trials, evaluation of the size of the sample; 6) analysis and modeling based on genomic data obtained by DNA and RNA sequencing. Next Generation Sequencing (NGS) and Third Generation Sequencing (TGS); 7) general concepts of high-throughput data analysis; 8) phylogenetic reconstruction.

The course will be organized in theoretical lectures and practice classes. The practice classes will require the active participation of students and will be devoted to train their abilities to solve problems and exercises and to apply to real data the methods introduced in the theoretical lectures (with the use of softwares such as Matlab, Python, or R).

Ad hoc slides will be used during the lessons and will be made available through the Portale della Didattica. Other material will be suggested in class and, if possible, made available through the Portale della Didattica. 


Modalità di esame: Prova scritta (in aula); Prova orale facoltativa;

Exam: Written test; Optional oral exam;

... The final exam will consists in a written test which will be divided in two parts: the former will be a multiple choice questionar, the latter will include some open-ended questions. The final grade will be given by the sum of the scores obtained in the two parts of the written test. If the sum of the two scores will be higher than 30, the final grade will be 30 with laude. An oral exam is optional, i.e., it may be only required by students with a grade higher than 18: the oral exam may however result in a variation of the grade that ranges from -3 to +3. The teachers of the course may also ask for an oral exam to further assess students knowledge.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.