# Modelling with Differential Equations

**Teacher**: dr. Josip Tambača, professor

**Semester**: second

**ECTS**: 6

Required course

- To introduce students to the application of mathematical modelling in the analysis of biomedical systems,
- To show how mathematics, especially partial differential equations and computing can be used in an integrated way to analyse biomedical systems.

- To have an enhanced knowledge and understanding of mathematical modelling and mathematical methods using ordinary and partial differential equations for the analysis of biological/medical systems,
- To be able to assess biological/medical inferences that rest on mathematical arguments,
- To be aware of the use of ordinary and partial differential equations and computers to assist them in studying biological/medical systems,
- To be able to formulate and analyse dynamical models of reaction kinetics,
- To apply Hodgkin-Huxley model to model ion transport,
- To use partial differential equations to model conservation, convection and diffusion in biomedical systems,
- To derive conclusions in biomedical models from the qualitative properties of the partial differential equations that model the phenomena,
- To formulate and apply models using partial differential equations on moving boundary problems.

**Reaction kinetics.**Michaelis-Menten kinetics, sigmoidal kinetics, oscillators and switches.**Dynamical behaviour of neuronal membranes.**Hodgkin-Huxley model, Fitzhugh-Nagumo model.**Introduction in partial differential equations in biology.**Conservation, convection, diffusion and attraction.**Traveling wave propagation.**Fisher’s equation.**Biological pattern formation.**Turing model. A chemical basis for morphogenesis.**Moving boundary problems.**Wound healing, tumour growth.