Computational Methods in Health Care Systems
- Unit Coordinator: Raffaele D'Ambrosio
- Programme: InterMaths
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: University of L'Aquila
- Language: English
- Delivery: In-class
- Aims:
Learning objectives.
The aim of the course is to provide knowledge and skills in the field of numerical modelling of Health Care systems, creating an effective bridge between the understanding of the continuous model, its qualitative properties and their counterparts in the discrete.
Learning outcomes.
At the end of the course, the student should
• have a deep knowledge and understanding of the most relevant computational techniques for the treatment of models in the Health Care field, together with aspects related to their implementation in accurate and efficient mathematical software;
• demonstrate the ability to evaluate the most appropriate discretization in relation to the problem to be solved and ability in theoretical analysis and mathematical software design;
• demonstrate ability to read and understand other texts on related topics. - Content:
Introduction to mathematical models for Health Care based on ordinary, stochastic and partial differential equations;
For each theme, the presentation will be twofold: presenting the continuous model, its qualitative properties and, jointly, presenting the most appropriate numerical approach to the approximation of solutions and the discrete conservation of the properties of the model.
Methods that preserve the positivity of solutions have particular relevance in this field.
In addition, advanced techniques of numerical linear algebra and optimization for large linear systems arising from semi-discretization of PDEs will be presented. - Pre-requisites:
Basic knowledge of Numerical Analysis, differential equations, linear algebra.
- Reading list:
- F. Brauer et al., Mathematical Epidemiology, Springer-Verlag (2008).
- J. D. Lambert, Numerical methods for ordinary differential systems: the initial value problem, John Wiley (1991).
- A. Quarteroni, Numerical Models for Differential Problems, Springer (2017).
- E. Isaacson, H.Keller, Analysis of numerical methods, Dover Publications (1994).
- W. Hundsdorfer, J. G. Verwer - Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations
- D.J. Higham and P. E. Kloeden, An Introduction to the Numerical Simulation of Stochastic Differential Equations, SIAM, 2021.
- Walter Gander, Martin J. Gander, Felix Kwok. Scientific Computing An introduction using Maple and MATLAB. Springer.
