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master's thesis
Matematički modeli kontrole dijabetesa
2023. urn:nbn:hr:166:606802
Zec, Ivana
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Zec, I. (2023). Matematički modeli kontrole dijabetesa (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:606802

Zec, Ivana. "Matematički modeli kontrole dijabetesa." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:606802

Zec, Ivana. "Matematički modeli kontrole dijabetesa." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:606802

Zec, I. (2023). 'Matematički modeli kontrole dijabetesa', Master's thesis, University of Split, Faculty of Science, accessed 15 April 2024, https://urn.nsk.hr/urn:nbn:hr:166:606802

Zec I. Matematički modeli kontrole dijabetesa [Master's thesis]. Split: University of Split, Faculty of Science; 2023 [cited 2024 April 15] Available at: https://urn.nsk.hr/urn:nbn:hr:166:606802

I. Zec, "Matematički modeli kontrole dijabetesa", Master's thesis, University of Split, Faculty of Science, Split, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:166:606802

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Metadata
TitleMatematički modeli kontrole dijabetesa
Title (english)Mathematical models for the menagment of diabates
AuthorIvana Zec
MentorAndrijana Ćurković (mentor)
Committee memberAndrijana Ćurković (predsjednik povjerenstva)
Committee memberMilica Klaričić Bakula (član povjerenstva)
Committee memberAna Laštre (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2023-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Ovaj rad proučava matematičke modele kontrole dijabetesa koji su dani sustavom običnih diferencijalnih jednadžbi, a razmatraju različitu problematiku kontrole dijabetesa. Opisana je ideja modela koji su kroz povijest donijeli neku novinu u matematičkom pogledu. Detaljnije je prezentiran matematički model dijabetesa tipa 1 koji proučava međusobnu interakciju koncentracije inzulina, koncentracije glukoze i koncentracije hormona rasta kod pojedinca, a čiji su parametri određeni eksperimentalno na grupi miševa. Glavni dio rada egzaktno rješava linearni populacijski model gdje promatramo broj osoba s dijabetesom u odnosu na broj osoba s njegovim komplikacijama. Posebno je razmatran dugoročni utjecaj stope razvoja komplikacija na rješenje modela. Rješenja ovog modela su isto tako prikazana grafički.
Abstract (english)
This graduation thesis studies the mathematical models of diabetes control given by the system of ordinary differential equations and considers various issues of diabetes control. The ideas of models that have brought something new in mathematical terms throughout history are described. More extensively a mathematical model of type 1 diabetes is presented that considers the mutual interaction of insulin concentration, glucose concentration and growth hormone concentration in an individual, and whose parameters were determined experimentally in a group of mice. The main part of the work solves the linear population model, where we observe the number of people with diabetes in relation to the number of people with its complications. In particular, the long-term influence of the complication development rate on the model solution is considered. The solutions of this model are also presented graphically.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:606802
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching, major in statistics and computing
Course: major in statistics and computing
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to authenticated users
Terms of useLicence In copyright icon
Created on2023-10-03 12:41:01