Population Dynamics
Code
11633
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Oleksiy Karlovych
Teaching language
Português
Objectives
At the end of this course students will have acquired basic knowledge and skills in the area of population dynamics/epidemiology in order to:
- Understand advanced contents in the area;
- Being able to start research on a topic in the area.
Subject matter
Depending on the interest of teacher and students, the program can be about evolutionary models (Hardy-Weinberg law, Fisher''s Theorem, Lotka-Volterra dynamics; Game theory. Static games and Nash equilibrium in games in normal form. Rationality. 2 players''s games. Dynamic games and evolutionarily stable strategies. The replicator dynamics. Games with continuous and compact set of strategies; Discrete Processes. Stochastic matrices and theorem of Perron-Frobenius. The Moran process. Final states and transient states. The coalescent. Evolutionary processes in graphs. The Wright-Fisher process; Diffusive approximations, the Kimura equations) or about epidemiology (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
N. Bacaër, A short history of mathematical population dynamics, Springer, 2011.
F. Brauer, P. van den Driessche, J. Wu, Mathematical Epidemiology, Springer, 2008.
N.F.Britton, Essential Mathematical Biology, Springer, 2003.
O. Diekmann and J.A.P. Heesterbeek, Mathematical Epidemiology of Infectious diseases,
John Wiley & Sons, 2000.
D.L. Hartle and A.G. Clark, Principles of Population Genetics. Sinauer, Massachussets, 2007.
J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge Univ. Press, Cambridge, UK, 1998.
J.H. Hubbard and B.H. West, Differential Equations: A Dynamical Systems Approach. Higher-Dimensional Systems, Springer, 1995.
M.A. Nowak, Evolutionary Dynamics: Exploring the Equations of Life, The Belknap Press of Harvard University Press, Cambridge, MA, 2006.
H.R. Thieme, Mathematics in Population Biology, Princeton University Press, 2003.