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Applications of Differential Equations in Biology - NMMA466

Title:	Aplikace diferenciálních rovnic v biologii
Form of teaching:	lecture
Guaranteed by:	Department of Software and Computer Science Education (32-KSVI)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2026
Duration in semesters:	1
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Maximum number of enrolled students:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Is provided by:	NMMA706
Additional information:	http://msekce.karlin.mff.cuni.cz/~prazak/vyuka/706/
Repeated enrollment:	2 / 2 / 2 / 2

Guarantor:	Karolína Korvasová, M.Sc., Dr. rer. nat.
Class:	M Bc. OM M Bc. OM > Doporučené volitelné
Classification:	Mathematics > Real and Complex Analysis, Topology and Category

Opinion survey results WS schedule Noticeboard

Annotation -

We derive some biological models (e.g. predator-prey models, epidemiological models, population models) and apply results of the theory of ordinary differential equations to these models.

Last update: Pyrih Pavel, doc. RNDr., CSc. (04.05.2018)

Course completion requirements -

The course is concluded with a written exam.

Last update: Korvasová Karolína, M.Sc., Dr. rer. nat. (13.05.2026)

Literature -

D. S. Jones, B. D. Sleeman: Differential equations and mathematical biology, Chapman & Hall, 2003.

J. D. Murray: Mathematical biology I: an introduction, Springer, 2002.

Last update: Bárta Tomáš, doc. RNDr., Ph.D. (23.05.2019)

Course assessment methods and requirements for successful completion, grading scheme -

Knowledge of the theory presented in the lectures, details at the web page of the lecturer.

Last update: Bárta Tomáš, doc. RNDr., Ph.D. (23.05.2019)

Syllabus -

1. Population models (Malthusian growth model, model with capacity of environment, Lotka--Volterra predator-prey model, Holling--Tanner, Gause's model with a shelter).

2. Epidemiologic models (SIR, SLIAR, SIR with space variable).

3. Game theory, replicator dynamics.

4. Models of chemical reactions (Michaelis-Menten, Turing patterns)

Last update: Korvasová Karolína, M.Sc., Dr. rer. nat. (13.05.2026)

Course registration requirements -

The course is a good supplement to the course Ordinary differential

equations NMMA333. We recommend the students who are not acquainted with

basic theory of ordinary differential equations to attend the course

NMMA706 instead.

Last update: Pyrih Pavel, doc. RNDr., CSc. (04.05.2018)