Deterministic modelling in population dynamics and epidemiology
Additional Info
- ECTS credits: 6
- University: University of L'Aquila
- Semester: 3
- Lecturer 1: Marco Di Francesco
- Lecturer 2: Simone Fagioli
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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".
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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.
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Prerequisites:
- Dynamical systems, numerical methods for ordinary differential equations.
- Linear partial differential equations of diffusive type.
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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.
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