1. Home
  2. NOVA School of Science and Technology
  3. Mathematics
  4. Statistics and Risk Management
  5. Populational Dynamics

Populational Dynamics

Objectives

The objectives of the course include:

 Part I

Further study of ordinary differential equation techniques.

Part II

- 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 analyze models for the transmission of infectious diseases using systems of differential equations.

General characterization

Code

12977

Credits

9.0

Responsible teacher

Paula Cristiana Costa Garcia Silva Patrício , Paulo José Fernandes Louro Ribeiro Doutor

Hours

Weekly - 4

Total - 60

Teaching language

Português

Prerequisites

This course assumes knowledge of analysis, differential equations, linear algebra. Some mathematical concepts useful for modeling will be introduced.

Bibliography

Part I:

1. M. Hirsch, S. Smale, R. Devaney, Differential Equations, Dynamical Systems & an Introduction to Chaos, Elsevier, 2004.

2. Chapters 1, 11, 14, 9, 21, 13 of the book A Short History of Mathematical Population Dynamics, by N. Bacaer (Springer 2011)

 

Parte II

1. Papers to be chosen

2. F. Brauer, P van den Driessche, J Wu, Mathematical Epidemiology, Springer, 2008

Teaching method

In theoretical-practical classes, topics and theoretical concepts will be presented. 
There will be problem solving. 

Book chapters will be proposed for preparation in articles or autonomy for presentation
 and discussion in class.

Evaluation method

40% - Evaluation corresponding to part I (homework, every week)

40% - Evaluation corresponding to part II (to be defined)

20% - Final seminar, in a topic to be defined by the student and teachers (not necessarily on the sylabus, but with the scope of the course).

Subject matter

Part I

- First-Order Equations

- Planar Linear Systems

- Phase Portraits for Planar Systems

- Classification of Planar Systems

- Higher Dimensional Linear Algebra

- Higher Dimensional Linear Systems

- Nonlinear Systems

- Equilibria in Nonlinear Systems

- Global Nonlinear Techniques

- Closed Orbits and Limit Sets

 

Part II: Mathematical models in epidemiology

Epidemic models - the model of Kermack-McKendrick
Models with demographic effects: SIR and SIS
Basic Reproduction Number, R0
Control
Generalizations:  temporary and partial immunity; age-structured models; spacial models; multi-strain models; vector-borne diseases