Deterministic modelling in population dynamics and epidemiology
- Code: DT0704
- Unit Coordinator: Marco Di Francesco, Antonio Esposito
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: University of L'Aquila
- Language: English
- Aims:
This course contributes to one of the learning objectives of the degree programmes in Mathematical Modelling and Mathematical Engineering, namely the formation of the student on advanced mathematical modelling in an interdisciplinary context, in particular in the biology/medicine area, more specifically in the field of mathematical modelling applied to the diffusion of epidemics, which is the main goal of the curriculum "Modelling and simulation of infectious diseases" of the degree program in Mathematical Modelling. Moreover, the course contributes to forming the student in the context of mathematical modelling applied to population dynamics, in agreement with the objectives of the curriculum "Mathematicla Models in Social Sciences" of the degree programme in Mathematical Modelling.
At the end of the course, the student
1) will be equipped with a sound knowledge on population dynamics modelling, particularly compartmental models which can also be applied in epidemiology.
2) will be able to formulate "ad-hoc" deterministic models, such as ordinary differential equations, partial differential equations, interacting particle systems, that describe the dynamics of an epidemics in specific situations.
3) will possess analytical techniques allowing to resolve the models studied and to determine the qualitative behaviour of the solutions to those models.
4) complement the models with auxiliary terms in order to plan specific "containment strategies" for epidemiological models.
- Content:
1) Introduction to population dynamics modelling via ODEs.
2) Introduction to epidemic modelling. The Kermack-McKendrick models and its variants.
3) Modelling of vector-borne diseases. Models with delay.
4) Computing the basic reproduction number.
5) Complex epidemics modelling, multi-group modelling.
Control strategies in ODE models.6) Age structured population models and applications in epidemiology. Class-Age structured models in epidemiology.
7) Spatial heterogeneity in population dynamics. Models with diffusion.
8) Reaction-diffusion systems. Travelling waves.
Lagrangian movements. Particle models. Nonlocal models. Discrete vs Continuum modeling using integro-differential equations.10) SIR (and variants) models with local and nonlocal diffusion.
11) Graph modeling for population dynamics
- Pre-requisites:
Dynamical systems, analytical methods for to resolutoin of ordinary differential equations.
Basics of linear partial differential equations. - 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.
Maia Martcheva - An Introduction to Mathematical Epidemiology; Texts in Applied Mathematics 61, Springer.
Lecture notes by the lecturer.
