Course: Mathematical Ecology and Epidemiology

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Course title Mathematical Ecology and Epidemiology
Course code UMB/340
Organizational form of instruction Lecture
Level of course Bachelor
Year of study not specified
Frequency of the course In each academic year, in the winter semester.
Semester Winter
Number of ECTS credits 3
Language of instruction Czech
Status of course Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Berec Luděk, doc. Ing. Dr.
  • Křivan Vlastimil, prof. RNDr. CSc.
Course content
1. Matematical modelling in biology 2. Population dynamics: unstructured models of single population, human population growth 3. Population dynamics: population with age structure, growth rate, sensitivity analysis 4. Population dynamics: harvesting models, harvest, pest control 5. Metapopulation dynamics: models of single population 6. Population interactions: predator-prey interaction, functional response, refugia 7. Population interactions: competition, principle of competitive exclusion 8. Population interactions: food webs, trophic cascade 9. Dynamics of infection diseases: basic epidemic model, epidemic control, some extensions 10. Dynamics of infection diseases: endemic diseases, rates of transmission 11. Macro-parasitic infections: general model, distribution of parasites, stabilizing and destabilizing mechanisms, schistosomiasis 12. Vector-borne infections: general model, possibilitz of infection eradication, Lyme disease, Zika virus, West Nile virus 13. Dynamics of infection diseases: evolution of virulence, evolution of resistence Part of the course is working with specific models in the R language.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Demonstration, Projection, Individual preparation for exam
  • Class attendance - 28 hours per semester
  • Preparation for classes - 28 hours per semester
  • Preparation for exam - 28 hours per semester
Learning outcomes
The aim of the course is to acquaint students with mathematical modelling in ecology, epidemiology, and other biologically oriented fields.
Mathematical biology is a unique discipline on the verge of mathematics and biology. The aim of mathematical biology is to use mathematical tools to understand, predict and manipulate biological phenomena and processes. It is thus complementary to biological experiments: it helps identify knowledge gaps, set up experimens, it draws from the results of experiments, substitutes experiments where experimenting is impossible or costly or generates hypotheses for further experimental work. Student will be able to explain advantages, but also limitations of mathematical modelling in biology, develop a number of simple models in ecology, epidemiology and other branches of biology, to work with such models and to analyze them, and to translate model results back into the language of biology.
Prerequisites
Basics of calculus, linear algebra and ordinary differential equations.
UMB/CV587
----- or -----
UMB/587

Assessment methods and criteria
Interview, Combined exam

elaboration of an individual project
Recommended literature
  • Keeling, Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.
  • Kot. Elements of mathematical ecology. Cambridge University Press, 2001.
  • Vynnycky, White. An introduction to infectious disease modelling. Oxford University Press, 2010.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses - Recommended year of study:-, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (2012) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Applied Mathematics (2010) Category: Mathematics courses 3 Recommended year of study:3, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses - Recommended year of study:-, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses - Recommended year of study:-, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses - Recommended year of study:-, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Winter