Course Unit


Deterministic modelling in population dynamics and epidemiology

  • 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.

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InterMaths Network
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)