Matematical Modelling in Biology and Medicine

mathematics

elementary

LECTURE

MA1_W01, MA1_W03

EXERCISES

MA1_K01, MA1_K02

(in Polish) Analiza I i II, Algebra Liniowa, RRZ, Rachunek P-stwa

The aim of the course is to introduce the basics of classical mathematical modeling in biology, epidemiology and medicine. In particular, the student will learn biological and medical applications of integrals and derivatives; equations and systems of ordinary differential equations modeling the development of populations, epidemics, and diseases; discrete models in genetics based on Markov chains. The student will also acquire basic skills in understanding models, their construction, their application in practice and their mathematical analysis.

The student knows and understands: (MA1_W01, MA1_W03)

W1.1 - using the derivative as the rate of change or gradient of a given quantity,

W1.2 - construction, applications and limitations of polynomial regression;

W2 - differential equation (dimension 1 or higher) which is a biological and epidemiological model, the concept of steady states, their stability and their importance in models; including models: exponential and logistic, L-V, SIR, their variants; other models;

W3 - basic discrete models which are numerical schemes for solving RRZ and discrete models based on Markov chains.

The student is able to (MA_W03, MA1_U01)

U1 - solve problems requiring the use of derivatives, integrals, research on the course of function variability in biological and epidemiological applications,

U2 - perform basic analysis of the RRZ-based model, its steady states, stability, interpret mathematical conclusions in a real context;

U3 - carry out basic analysis of a model based on a Markov-type process, its absorbing states, expected value;

The student is ready: (MA1_K01, MA1_K02)

K1 - prepare a paper presenting a new issue,

K2 - participate in a scientific discussion.

For all effects, the following assessment criteria are adopted for all forms of verification:

grade 5: fully achieved (no obvious shortcomings)

grade 4.5: achieved almost fully and criteria for awarding a higher grade are not met

grade 4: largely achieved and the criteria for a higher grade are not met

grade 3.5: largely achieved - with a clear majority of positives - and the criteria for granting a higher grade are not met

grade 3: achieved for most of the cases covered by the verification and criteria for a higher grade are not met

grade 2: not achieved for most of the cases covered by the verification