H. Malchow: Compact Course Anlage 3
Dr. Horst Malchow
Professor of Applied Systems Science Institute of Environmental Systems Research Department of Mathematics and Computer Science University of Osnabr¨uck
49069 Osnabr ¨uck, Germany
2 February 2012 Tel/Fax +49-541-969-2499/2599
E-Mail malchow@uos.de
Internet www.usf.uos.de/∼malchow
Mathematical Modelling in Population Dynamics
Compact Course and Exercises
I.
Lecture Programme
1. Introduction
1.1 Why mathematical modelling?
1.2 From systems analysis to model schemes and mathematics 1.3 Model classes, analytical and numerical methods
1.4 Recommended textbooks, cf. chap. (II.)
2. Environmental systems and compartments
2.1 Linear differential equations
2.2 Explicit solution of selected problems
3. From chemical kinetics to biological dynamics
3.1 Order of chemical reactions and formal kinetics 3.2 Nonlinear differential equations
3.3 Stationary solutions and their stablity 3.4 Models of enzyme kinetics
3.5 Translation of chemical into biological language
4. Population growth
4.1 Continuous vs. discrete time
4.2 Linear, exponential and logistic growth
4.3 Logistic growth and harvesting with maximum sustainable yield 4.4 Allee effect
H. Malchow: Lecture Programme Anlage 3
5. Population growth and interactions
5.1 Mutualism, predation and competition
5.2 Functional response of predators to prey abundance, Holling types 5.3 Holling-type II: Oscillations
5.4 Holling-type III: Oscillations and excitability 5.5 Periodic environments and deterministic chaos 5.6 Aperiodic dynamics of multi-species systems 5.7 Intra- and interspecific competition
5.8 Transmission of infectious diseases
6. Population growth and movement
6.1 Continuous vs. discrete space 6.2 Interaction, diffusion and advection
6.3 Exponential and logistic growth as well as bistable systems with diffusion 6.4 Diffusive front speeds
7. Population growth, interactions and movement
7.1 Diffusive and advective instabilites of spatially uniform population distributions 7.2 Turing structures
7.3 Branching and net structures 7.4 Target patters and spiral waves
7.5 Heterogeneous environments, spatiotemporal chaos 7.6 Biological invasions and spread of infectious diseases
II.
Recommended textbooks
ALLEN, L. J. S. (2007). An introduction to mathematical biology. Upper Saddle River NJ: Pearson Education.
AUGER, P., LETT, C. & POGGIALE, J.-C. (2010). Mod´elisation math´ematique en ´ecologie. IRD
´
Editions. Paris: Dunod.
BRITTON, N. F. (2003).Essential mathematical biology. Berlin: Springer.
EDELSTEIN-KESHET, L. (2005). Mathematical models in biology, vol. 46 ofClassics in Applied Math-ematics. Philadelphia: The Society for Industrial and Applied MathMath-ematics.
MALCHOW, H., PETROVSKII, S. V. & VENTURINO, E. (2008).Spatiotemporal patterns in ecology and
epidemiology: Theory, models, simulations. CRC Mathematical and Computational Biology Series. Boca Raton: CRC Press.
H. Malchow: Compact Course Anlage 3
MURRAY, J. D. (2003). Mathematical biology. II. Spatial models and biomedical applications, vol. 18 ofInterdisciplinary Applied Mathematics. Berlin: Springer.
OKUBO, A. & LEVIN, S. (2001). Diffusion and ecological problems: Modern perspectives, vol. 14 of Interdisciplinary Applied Mathematics. New York: Springer.
VRIES, G., HILLEN, T., LEWIS, M., M ¨ULLER, J. & SCHONFISCH¨ , B. (2006). A course in mathemat-ical biology: Quantitative modeling with mathematmathemat-ical and computational methods. Mathematmathemat-ical Modeling and Computation. Philadelphia: Society for Industrial and Applied Mathematics.
Osnabr¨uck, 2 February 2012 H. Malchow
