Mathematical Models in Epidemiology
Code
10854
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
3.0
Teacher in charge
Paula Cristiana Costa Garcia Silva Patrício
Weekly hours
2
Total hours
28
Teaching language
Português
Objectives
The objectives of the course include:
- basic knowledge of the terms and principles in epidemiology
- basic knowledge of the main results of the theory of mathematical models for the transmission of infectious deonças
- ability to build and analyse models for the transmission of infectious diseases using systems of differential equations
- estimation of the parameters of the models for the transmission of infectious diseases
- use of R-project software for the mathematical and statistical analysis os the various models for the transmission of infectious diseases
Prerequisites
This course assumes knowledge of analysis, differential equations, linear algebra, probability and statistics. Some mathematical concepts useful for modeling will be introduced.
Subject matter
- Epidemic models - the model of Kermack-McKendrick
- Models with demographic effects: SIR and SIS
- Basic Reproduction Number, R0
- Control
- Generalizations:
- SEIR models
- Diseases in animal populations
- Models with Heterogeneity
Bibliography
- F. Brauer, P van den Driessche, J Wu, Mathematical Epidemiology, Springer, 2008
- H.R. Thieme, Mathematics in Population Biology, Princeton Series in Theoretical and Computational Biology
- O Diekmann, J A :P Heesterbeek, Mathematical Epidemiology of Infectious diseases, Whiley 2000
- H. Weiss, A mathematical introduction to population Dynamics, Publicações matemáticas do IMPA
- M. W. Hirsch, S. Smale, R. L. Devaney, Differential Equations, Dynamical Systems & an introduction to chaos, Academic Press. Elsevier, 2003
- J. H. Hubbard, B. H. West, Differential Equations: A Dynamical Systems Approach. Higher-Dimensional Systems, Springer-Verlag, 1995.
Teaching method
Theoretical and practical exposure to the subject and introducing examples.
Exercises for resolution on autonomy with adapted bibliography .
Questions and development of each topic will be under tutorial.
Evaluation method
Evaluation is based on:
3 worksheets for solving at home and delivery for correction / discussion (75%)
1 final written work on one of the proposed topics to be presented and discussed in a final presentation (25%)
Frequency is given to students who deliver the resolutions of 2 of the 4 exercises/final work proposed in time
The three worksheets and final work can be replaced by a final exame.
More detailed rules are available in the Portuguese version.