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master's thesis
SIS i SIR epidemiološki modeli temeljeni na Markovljevim lancima u diskretnom vremenu
2021. urn:nbn:hr:126:224744
Štivić, Ira
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Štivić, I. (2021). SIS i SIR epidemiološki modeli temeljeni na Markovljevim lancima u diskretnom vremenu (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:224744

Štivić, Ira. "SIS i SIR epidemiološki modeli temeljeni na Markovljevim lancima u diskretnom vremenu." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:224744

Štivić, Ira. "SIS i SIR epidemiološki modeli temeljeni na Markovljevim lancima u diskretnom vremenu." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:224744

Štivić, I. (2021). 'SIS i SIR epidemiološki modeli temeljeni na Markovljevim lancima u diskretnom vremenu', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 25 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:224744

Štivić I. SIS i SIR epidemiološki modeli temeljeni na Markovljevim lancima u diskretnom vremenu [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2021 [cited 2024 December 25] Available at: https://urn.nsk.hr/urn:nbn:hr:126:224744

I. Štivić, "SIS i SIR epidemiološki modeli temeljeni na Markovljevim lancima u diskretnom vremenu", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:126:224744

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Metadata
TitleSIS i SIR epidemiološki modeli temeljeni na Markovljevim lancima u diskretnom vremenu
Title (english)SIS and SIR Epidemic Models Based on Markov Chains in Discrete Time
AuthorIra Štivić
MentorNenad Šuvak (mentor)
Committee memberDanijel Grahovac (predsjednik povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
Committee memberIvan Papić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2021-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
U ovom radu opisani su SIS i SIR epidemiološki modeli temeljeni na Markovljevim lancima u diskretnom vremenu. U uvodu je objašnjena uloga Markovljevih lanaca u matematici, kao i u primjeni na biološke procese. Prvo poglavlje sadrži važne definicije i svojstva Markovljevih lanaca, te primjere koji prikazuju kako se navedena teorija koristi. U sljedećem poglavlju navodimo diferencijske jednadžbe kojima su opisani jednostavni SIS i SIR epidemiološki modeli, diferencijske jednadžbe koje deterministički SIS i SIR epidemiološki modeli zadovoljavaju, te važnost ovakvih modela u primjeni. Zatim su detaljnije opisani stohastički SIS i SIR epidemiološki modeli, diferencijske jednadžbe na kojima se temelje, te neka važna svojstva navedenih modela. U posljednjem poglavlju dajemo nekoliko simulacija stohastičkih modela obrađenih u ovom radu.
Abstract (english)
This paper describes SIS and SIR epidemic models based on discrete time Markov chains. In the introduction, we explain the role of Markov chains in mathematics, as well as in application to biological processes. The first chapter contains important definitions and properties of Markov chains, as well as some examples which illustrate the use of Markov theory. In the next chapter we state some differential equations which describe simple SIS and SIR epidemic models, differential equations which deterministic SIS and SIR epidemic models satisfy and the importance of these models in application. Then, we describe the stohastic SIS and SIR epidemic models in more detail, differential equations on which they are based on and some important properties of these listed models. In the final chapter, we give a few simulations of the stohastic models covered in this paper.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:224744
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical 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 on2021-10-25 11:18:39