Category Archives: Course

The lecture presents a wide area of applications of nonlinear mathematical modeling in biomedical applications.

UWAGA: Zajęcia 12.04 są odwołane!

Slides from lectures (in Polish)

Wyklad1 – Modele kompartmentowe i ich zastosowania w hemodializie
Wyklad2 – Modele membranowe: pasywny transport wody i substancji przez błony sztuczne i biologiczne
Wyklad3 – Modele reakcji-dyfuzji: czasoprzestrzenny opis transportu
Wyklad4 – Modele transportu w dializatorach do oczyszczania krwi (Dane do wykładu 4)
Wyklad5 – Modele rozłożone transportu wody i substancji w tkance (Dane do wykładu 5)
Wyklad6 – Model liniowo-kwadratowy w radioterapii nowotworów

Dodatkowe pliki do pobrania:
ControlGroupZajecia.csv
enzymeData.csv

The lecture is devoted to the widely understood mathematical modeling in biology and medicine. We mainly focus on ecological models which are built using differential and difference equations. We also consider models of immune reactions and those of classical genetics (Mendel theory) based on Markov chains.

News:
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The lecture presents a wide area of applications of nonlinear mathematical modeling in biology, medical science and clinical medicine.

Computer laboratory classes are based on MATLAB® software and are aimed at the presentation of computer methods for simulation and analysis of solutions of ordinary differential equations and equations with discrete time. Students have an opportunity to investigate the models themselves.

Slides from computer labs:
compLab1 – Introduction to MATLAB
compLab2 – Migrations in logistic equation, Alee effect, Holling response
compLab3 – Discrete logistic equation (solutions, bifurcations), two dimensional discrete models
compLab4 – Classic L-V (solutions, average value, harvesting), L-V with logistic term
compLab5 and data – Interactions between populations (competition/mutualism), May model
compLab6 – Lorenz attractor (solutions, behavior)
compLab7 – Kinetics of single enzyme and product, kinetics of multiple enzymes/prodicts/substrates
compLab8 – Zeeman model for the heartbeat
compLab9 – Models with various types of antigens
compLab10 – Kuznetsov model (solutions, behavior)
compLab11 – TC model of hemodialysis, data fitting
compLab12 – Basic gene expression models, part of p53 signaling pathway
compLab13 – Logistic model with vaccinations, L-V with harvesting
compLab14 – Model of self-repressing gene, Mackey-Glass model
compLab15 – Projects presentations