Mathematical models in biology

There are no prerequisites.

Fundamental principles of mathematical modeling, biological motivation.
Discrete models of population dynamics. Stability in linear and nonlinear systems, Leslie matricial model, models for a single population, discrete models for interacting populations (models of parasitism and mutualism, competition, and epidemiological models).
Stochastic models in biology. Application of probability theory in ecology (Mendelian heritage, lineage extinction), Fundamental genetic models (Hardy-Weinberg and Fisher-Haldane-Wright law), evolutionary models.
Continuous models in biology. Application of dynamical systems in population dynamics, stability in linear and nonlinear systems (Lyapunov theory), various growth models, fundamentals of Poincare-Bendixson theory, predator-prey models (Lotka-Volterra), models of symbiosis, of competition, and their generalizations, concrete ecological and epidemiological models (biodiversity, systems of type SIR), molecular kinetics (Menten-Michaelis) and basic neurological models (Hodgkin-Huxley, Fitzhugh-Nagumo).

1. L. J. S. Allen: An introduction to mathematical biology, Upper Sadle River : Pearson, cop. 2007.
2. N. F. Britton: Essential mathematical biology, London : Springer, cop. 2003.
3. L. Edelstein-Keshet: Mathematical models in biology, Philadelphia : Society for Industrial and Applied Mathematics, cop. 2005.
4. A. W. F. Edwards: Foundations of mathematical genetics, 2nd ed., Cambridge : Cambridge University Press, 2000.
5. J. D. Murray: Mathematical biology, 3rd ed., New York : Springer, cop. 2002-2003.

The main goal is the application of already obtained mathematical knowledge to the description of biological processes. The student will be prepared to the interdisciplinary work and to the collaboration with experts from other disciplines.

Knowledge and understanding:
To achieve understanding of principles of mathematical modeling in science. To be
acquainted with basic biological models.
Application:
Formulating and solving simple problems in biology (modeling, forecasting o!!f phenomena).
Reflection:
Through various examples one begins to appreciate the applicability of mathematics in science.
Transferable skills:
One can learn how to describe biological (and other) processes using mathematical language and achieve a general feeling for mathematical applications. The goal is also to develop the skills for using existent literature and various computer programs.

Lectures, exercises, homeworks, consultations

Presentation of home exercises
2 midterm exams instead of written exam, written exam
Oral exam
Estimating working knowledge on two midterm tests, home exercises and possible on the written test as well as estimating theoretical knowledge on the final oral exam.
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Jasna Prezelj:
PREZELJ, Jasna, VLACCI, Fabio. An interpolation theorem for slice-regular functions with application to very tame sets and slice Fatou–Bieberbach domains in H2, AMPA, ISSN 0373-3114, 2022, vol. 201, no. 5, str. 2137-2159 [COBISS-SI-ID - 106389763]
GENTILI, Graziano, PREZELJ, Jasna, VLACCI, Fabio, Slice conformality and Riemann manifolds on quaternions and octonions,: Mathematische Zeitschrift. - ISSN 0025-5874, 2022, vol. 302, no. 2, str. 971-994 [COBISS-SI-ID - 117983235]
GENTILI, Graziano, PREZELJ, Jasna, VLACCI, Fabio, On a definition of logarithm of quaternionic functions, JCNG 2023, vol. 17, no.3, str. 1099-1128 [COBISS-SI-ID - 162763779]