MathMods :: Joint MSc

Additional Info

• ECTS credits: 6
• University: University of L'Aquila
• Semester: 3
• Lecturer 1: Marco Di Francesco
• Lecturer 2: Simone Fagioli
• Objectives:

   

  • 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".
• Topics:

   

  • 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.
• Prerequisites:

   

  • Dynamical systems, numerical methods for ordinary differential equations.
  • Linear partial differential equations of diffusive type.
• Books:

   

  • 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.