Modelos Matemáticos em Biomedicina

Objectives

The students will gain conceptual and technical skills in mathematical modeling for biomedical questions and applications. They will increase their knowledge on the use of numerical analysis and applied analysis for infection processes, epidemiology, cancer dynamics, blood flow models. They will gain hands-on experience on the implementation of numerical methods using dedicated software and generate their own codes for specific model investigation and simulation. Critical thinking on modeling and model links to biomedical data will be fostered during the course.

Syllabus

Fundamentals of model building, analysis and simulation in biomedicine. Ordinary Differential Equations (ODE) models for population dynamics in medicine and epidemiology: SI, SIR, SIS, infection dynamics and control. Asymptotic analysis and numerical approximation. Model fitting to data. Partial differential equation (PDE) models for spatial processes in biomedicine: Tumor dynamics and spread. Atherosclerosis. Blood flow modeling. Computational methods. Multiscale models.

Prerequisites

AL, CDI1, CDI2 - General Mathematics, MC - Numerical Analysis and Applied Analysis.

Cross Competence Component

The UC allows the development of transversal competences on Critical Thinking, Creativity and Problem Solving Strategies, in class, in autonomous work and in the several evaluation components. The percentage of the final grade associated with these competences should be around 15%.

Programming And Computing Component

Computational project (50% of the evaluation).

Ethical Principles

All members of a group are responsible for the group’s work. In any assessment, every student shall honestly disclose any help received and sources used. In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.