Mathematical models in biology (2008/2009)

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Course code
Name of lecturers
Marco Squassina, Antonio Marigonda
Marco Squassina
Number of ECTS credits allocated
Academic sector

Language of instruction
3° Q dal Apr 20, 2009 al Jun 19, 2009.

Lesson timetable

3° Q
Day Time Type Place Note
Tuesday 11:30 AM - 1:30 PM lesson Lecture Hall E  
Wednesday 4:30 PM - 6:30 PM lesson Lecture Hall E  
Thursday 3:30 PM - 5:30 PM lesson Lecture Hall E  

Learning outcomes

Understanding of the main mathematical tools, local and global, analytical and geometrical, necessary for the study of mechanical and biological models based upon equations and systems of ordinary differential equations.
Understanding of the main evolutionary models of one or more interacting populations, both in a discrete and continuous setting. Understanding of physical, medical and neurological models.


First section:

General features of discrete and continuous dynamical systems. Linear and nonlinear systems, integrability, flow, first integrals. Equilibria and stability, eigenvalue analysis, Lyapunov function. Euler-Lagrange equations, Legendre transforms, Hamilton equations and Hamiltonian systems. Application to biological model of populations growth of logistic or Malthusian type, the Lotka-Volterra predator-prey system. Modelization and analysis of some physical phenomena.

Second section:
Equations and systems of PDE of parabolic type which emerge in mathematical biology, in particular reaction-diffusion systems of Lodka-Volterra type. Trapping regions. Qualitative behaviour of dynamics.

The course includes various numerical simulations of the models we consider, which will be included into 12 extra laboratory lectures.

Some extra one-hour lectures complementing the topics of the course could be available, held by external teachers.

The course is mainly based upon:

For the first part:

Introduzione all'Analisi Qualitativa delle Equazioni Differenziali Ordinarie
Marco Squassina, Simone Zuccher
Apogeo Editore 2008, ISBN 9788850310845

For the second part:

Smoller, Joel
Shock waves and reaction-diffusion equations / Joel Smoller . - 2. ed. - New York [etc.] : Springer, c1994. - XXII, 632 p. ; 25 cm.

Reference books
Author Title Publisher Year ISBN Note
M. Squassina, S. Zuccher Introduzione all'Analisi Qualitativa delle Equazioni Differenziali Ordinarie. 332 pagine, 365 figure. Apogeo Editore 2008 9788850310845
J. Murray Mathematical Biology Springer 2002 0-387-95223-3
G. Gaeta Modelli Matematici in Biologia Springer 2007 978-0-7923

Assessment methods and criteria

Final oral examination.

Teaching aids