Being able to solve stationary partial differential equations numerically, analyse the quality of numerical solutions, select proper methods and implement them in a computer program.

Tumor initiation, progression and invasion are complex processes involving multiple and different phenomena. Mathematical models and computer simulations can help to describe, schematize and comprehend them, to provide data which could be putatively used in clinical practice to prevent and/or more specifically treat cancer. In this context, a multidisciplinary approach is fundamental to reach this goal. The main objective of this course is to approach and understand the biological processes at the base of cancer, focusing on the most significant features of oncogenesis, with the aim to provide basic information which can be applied to mathematical modelling. On completion, the student should:

• know fundamentals about structure and functions of nucleic acids and proteins in eukaryotic cell;
• understand the significance of gene mutations and epigenetics alterations in diseases;
• identify tumor classification criteria;
• understand biological and functional mechanisms at the base of cancer initiation and progression; -
• know the most important databases for DNA mutation classification, microRNA and protein pathway analysis as well as on-line resources for acquiring datasets to be applied to big data analysis,
• know and understand the principles at the base of personalized therapy in cancer to predict the response to therapeutic schemes.

The aim of this course is to provide students with basics about modeling, analysis and control of networked and multi-agent systems through consensus techniques.

This course contributes to one of the learning objectives of the degree programmes in Mathematical Modelling and Mathematical Engineering, namely the formation of the student on advanced mathematical modelling in an interdisciplinary context, in particular in the biology/medicine area, more specifically in the field of mathematical modelling applied to the diffusion of epidemics, which is the main goal of the curriculum "Modelling and simulation of infectious diseases" of the degree program in Mathematical Modelling. Moreover, the course contributes to forming the student in the context of mathematical modelling applied to population dynamics, in agreement with the objectives of the curriculum "Mathematicla Models in Social Sciences" of the degree programme in Mathematical Modelling.

At the end of the course, the student 

1) will be equipped with a sound knowledge on population dynamics modelling, particularly compartmental models which can also be applied in epidemiology.

2) will be able to formulate "ad-hoc" deterministic models, such as ordinary differential equations, partial differential equations, interacting particle systems, that describe the dynamics of an epidemics in specific situations.

3) will possess analytical techniques allowing to resolve the models studied and to determine the qualitative behaviour of the solutions to those models.

4) complement the models with auxiliary terms in order to plan specific "containment strategies" for epidemiological models.