Unit Coordinator: Marco Di Francesco, Simone Fagioli
Programme: Erasmus Mundus
ECTS Credits: 6
Semester: 1
Year: 2
Campus: University of L'Aquila
Language: English
Aims:
Enabling the student to formulate "ad-hoc" deterministic models, such as ODEs, PDEs, interacting particle systems, that describe the dynamics of an epidemics in specific situations.
Providing analytical and numerical techniques allowing to determine the qualitative behaviour of those models.
Complement the models with "control" terms in order to plan specific "containment strategies".
Content:
Introduction to epidemic modelling.
SIR models and their variants.
Multi group modelling.
Simulation of SIR and SEIR models.
Control methods based on drug therapy.
Models with time delaly, asymptotic behavior and stability.
Spatial models for the spread of an epidemic.
Control strategies based on wave propagation.
Interactin particle systems for the evolution of epidemics.
Discrete vs Continuum modeling using integro-differential equations.
Simulation of multi-agent systems.
Computation of Rt from numerical simulations.
Control and optimisation strategies based on lockdown and drug therapy.
Pre-requisites:
Dynamical systems, numerical methods for ordinary differential equations.
Linear partial differential equations of diffusive type.
Reading list:
James D. Murray; Mathematical biology I: An introduction; Springer.
James D. Murray; Mathematical biology II: Spatial Models and biomedical applications; Springer.
Fred Brauer, Pauline van den Driessche, Jianhong Wu; Mathematical Epidemiology; Lecture notes in mathematics; Springer.
A network of 12 European Universities, coordinated by Department of Information Engineering, Computer Science and Mathematics (DISIM) at University of L'Aquila in Italy (UAQ)
