Unit MATHEMATICAL MODELS FOR APPLICATIONS
- Course
- Mathematics
- Study-unit Code
- 55A00070
- Curriculum
- Didattico-generale
- Teacher
- Silvana De Lillo
- Teachers
-
- Silvana De Lillo
- Hours
- 42 ore - Silvana De Lillo
- CFU
- 6
- Course Regulation
- Coorte 2020
- Offered
- 2020/21
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Academic discipline
- MAT/07
- Type of study-unit
- Opzionale (Optional)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Elements of poulation dynamics.Examples of single specie and two-species models.Elements of modeling of infectious deseases.Elements of the Kinetic theory of active particles.Applications to complex living systems.
- Reference texts
- Nicholas F.Britton "Essential Mathematical Biology".Springer
Nicola Bellomo "Modeling Complex Living Systems" Birkhauser - Educational objectives
- Following this course a student is expected to get the skills to solve some fundamental initial value problem for population dynamics for one or two species,discussing the nature of stationary points..Moreover he/she should be able to solve problems associated with the spread of infectious deseases.The student will also get acquainted with the Kinetic Theory of active particles.In such framework applications to the modeling of complex living systems will be discussed.
- Prerequisites
- We require the student to be acquainted (from previous mathematical analysis courses) with the methods of solution for I and II order ordinary differential equations with constant coefficients.Moreover it is required to have familiarity with fundamental elements of the theory of partial differential equations,such as their classification and the solution of simple problems through the Fourier series approach.
- Teaching methods
- Lectures at the blackboard. Slides. Office hours
- Other information
- Some didactic material will be distributed among the students
during the course,in order to facilitate the understanding of the lectures. - Learning verification modality
- Oral exam, with questions on the theoretical part of the course and discussion of some practical example.The exam will last for about 5o minutes.Its aim is to verify: i) the rigour of logic acquired by the student; ii)his/her ability to handle new mathematical techniques; iii) his/her ability to synthetise.
- Extended program
- Techniques for difference equations.Graphical analysis.Bifurcations.Systems of linear equations:Jury conditions.Linear and nonlinear first order time models.Insect population dynamics models.Differential equations models.Evolutionary aspects.Fibonacci rabbits..Euler-Lotka equations. Population dynamics of interacting species.Host-Parasitoid interactions.The Lotka-Volterra system.
Introduction to the modelling of infectous diseases.The Simple Epidemic and S.I.S. diseases.S.I.R. epidemics.S.I.R. endemics.Eradication and control.
Complex systems.Kinetic theory of active particles.Applications of the KTAP theory .A traffic flow model. A model of epidemics diffusion. Social dynamics and a model of learning.