Matematičko modeliranje bioloških sustava

master's thesis

• Author: Nina Pospišil
• Mentor: Igor Pažanin (mentor)
• Committee member: Igor Pažanin (predsjednik povjerenstva)
• Committee member: Miljenko Marušić (član povjerenstva)
• Committee member: Goran Radunović (član povjerenstva)
• Committee member: Boris Muha (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu predstavljeni su matematički modeli za tri biološka sustava. Proučavanjem evolucije populacije, stanične dinamike i razvoja epidemijskih bolesti dolazimo do zaključka da navedene biološke sustave dobro opisuju sustavi običnih diferencijalnih jednadžbi. U analizi modela populacijske genetike dolazimo do zaključka da nasumično parenje uz ostale pretpostavke osnovnog modela nasumičnog parenja vode do očuvanja genetičke raznolikosti unutar populacije. Kada neka od pretpostavki modela nije ispunjena smatramo da dolazi do evolucije genetičke strukture populacije. S obzirom na globalno zatopljenje i sve većeg straha od cijepljenja postoji izrazita potreba za preciznim modelima razvoja epidemijskih bolesti. S time na umu, pokazali smo na koji način za svaku bolest za koju postoji cjepivo možemo izračunati potrebnu procijepljenost za efikasno sprječavanje epidemije. Zadnje poglavlje daje vrlo važnu informaciju za efikasna istraživanja na području stanične dinamike. Kako bi se smanjili troškovi eksperimentalnih mjerenja za potrebe istraživanja stanične dinamike, kvantitativni model metaboličkih sustava određuje minimalan broj unutarstaničnih bioreakcija koji opisuju sve značajne bioreakcije te stanice.

Abstract (english)

This thesis presents mathematical models for three biological systems. The analysis of biological systems in population genetics, epidemiology and cellular dynamics has led us to the conclusion that they can be well described by ordinary differential equations. Population genetic model analysis showed that random pairing with other assumptions of the basic model of random mating leads to the preservation of genetic diversity within the population. When some of the assumptions of the model are not fulfilled, we consider the evolution of the genetic structure of the population. The aim of the second chapter is to give an elementary introduction to mathematical models that are used to explain epidemiologic phenomena and to assess vaccination strategies. Given the present trends in global warming, there is a need to predict the dynamics and transmission of mosquito-borne diseases with greater accuracy and over longer periods of time, both in constant and growing populations. In metabolic flux analysis an important issue concerns the number of distinct bioreactions that are generated when computing the EFMs. It may become very large because it combinatorially increases with the size of the underlying metabolic network. Therefore, there is clearly a need for reducing the model size as much as possible and trying to determine a minimal subset of bioreactions that are able to fully describe the available experimental data.

• Keywords: biološki sustavi; sustavi običnih diferencijalnih jednadžbi; modeli populacijske genetike; modeli razvoja epidemijskih bolesti; model metaboličkih sustava
• Keywords (english): biological systems; ordinary differential equations; population genetic model analysis; epidemiologic phenomena development models; metabolic flux analysis
• Language: croatian
• URN:NBN: urn:nbn:hr:217:690868
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-06-11 12:00:11