Mathematical Models in Biology

Aim

After completing the course the student should be able to communicate, apply, model, analyze and solve problems by using the concepts and methods described in the course content.

Content

Modeling with ordinary differential equations and time continuous dynamical systems. Phase portraits and stability of equilibrium points. Applications: models for population dynamics and ecosystems, chemostat, Lotka-Volterra models for predator-prey and competing populations, SIR and other epidemic models, neural impulses. Modeling with difference equations och time discrete dynamical systems. Equilibrium points and stability, the logistic map, cobweb diagrams. Applications: models for population dynamics, epidemiska modeller, population genetics, Leslie matrices and population structures. Modeling with partial differential equations. The continuity equation and diffusion equations, Fourier series in one and several dimensions, separation of variables. Applications: aggregation models, the Turing model for diffusion driven instability in chemical reactions and pattern formation.