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master's thesis
Numerička i teorijska analiza epidemiološkog SIR modela i inačica
Zagreb: University of Zagreb, Faculty of Science, 2021. urn:nbn:hr:217:003845
Pleskina, Marijeta
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Pleskina, M. (2021). Numerička i teorijska analiza epidemiološkog SIR modela i inačica (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:003845

Pleskina, Marijeta. "Numerička i teorijska analiza epidemiološkog SIR modela i inačica." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:003845

Pleskina, Marijeta. "Numerička i teorijska analiza epidemiološkog SIR modela i inačica." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:003845

Pleskina, M. (2021). 'Numerička i teorijska analiza epidemiološkog SIR modela i inačica', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:003845

Pleskina M. Numerička i teorijska analiza epidemiološkog SIR modela i inačica [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2021 [cited 2024 November 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:003845

M. Pleskina, "Numerička i teorijska analiza epidemiološkog SIR modela i inačica", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:217:003845

Metadata
TitleNumerička i teorijska analiza epidemiološkog SIR modela i inačica
Title (english)Numerical and theoretical analysis of epidemiological SIR models and variants
AuthorMarijeta Pleskina
MentorMarko Erceg (mentor)
Committee memberMarko Erceg (predsjednik povjerenstva)
Committee memberMladen Vuković (član povjerenstva)
Committee memberMarko Horvat (član povjerenstva)
Committee memberIvica Nakić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2021-12-02, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu predstavljen je epidemiološki SIR model te nekoliko njegovih inačica, kao što su SIRS, SIS i SEIR modeli. Osim teorijskom analizom sustava običnih diferencijalnih jednadžbi modela, rad se bavi i metodama za procjenu parametara modela iz dostupnih podataka, uz primjenu na pandemiju koronavirusa. Opisane su neke metode za numeričko rješavanje jednadžbi. Napravljena je analiza stacionarnih točaka sustava u čiju je svrhu korišten Routh-Hurwitz kriterij stabilnosti. Osnovni reprodukcijski broj \(R_0\) predstavljen je kao bitan parametar koji odreduje hoće li doći do epidemije ili ne. Osim klasičnog SIR modela, obrađene su njegove inačice s nekonstantnim parametrima te uz vitalnu dinamiku.
Abstract (english)
This thesis presents the epidemiological SIR model and several variants of it, such as the SIRS, SIS and SEIR models. In addition to the theoretical analysis of the system of ordinary differential equations of the model, the thesis also deals with methods for estimating the model parameters from the available data, with application to the coronavirus pandemic. A few methods for numerical solution of the equations are described. An analysis of the equilibrium points of the system was made, using the Routh-Hurwitz stability criterion. The basic reproduction number \(R_0\) is presented as an important parameter that determines whether an epidemic will occur or not. In addition to the classic SIR model, its versions with non-constant parameters and with vital dynamics are described.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:003845
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-12-15 13:41:42