Principles of Mathematical Modelling


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Principles of Mathematical Modelling

Code: 239976
ECTS: 6.0
Lecturers in charge: prof. dr. sc. Miljenko Marušić
Take exam: Studomat

1. komponenta

Lecture typeTotal
Lectures 30
Exercises 30
* Load is given in academic hour (1 academic hour = 45 minutes)
1. To introduce students to the application of mathematical modelling in the analysis of biomedical systems including populations of molecules, cells and organisms.
2. To show how mathematics, especially ordinary differential equations and computing can be used in an integrated way to analyse biomedical systems.

1. Introduction to continuous models.
2. Population dynamics. Single-species populations. Malthus (exponential) model, Verhulst (logistic) model, Gompertz model. Mathematical models of tumour growth
3. Modelling loss of population (death, harvesting). Growth under restriction. Monod model. Chemostat model.
4. Parameter identification problem. Least squares method. Elements of numerical optimization.
5. Numerical solution of ODE.
6. Steady state solutions, stability, linearization. Systems of equations, phase-plane diagrams.
7. Population dynamics. Multiple species populations. Predator-prey systems, Lotka-Volterra model. Competition models.
8. Population biology of infectious diseases. SIR model.
9. Linear difference equations with applications. Qualitative behaviour. Cell division, an insect population.
10. Nonlinear difference equations with applications. Steady states, stability. Logistic difference equation. Density dependence, Nicholson-Bailey model.
1. semester
Mandatory course - Regular study - Biomedical Mathematics
Consultations schedule: