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master's thesis
SIS i SIR epidemiološki modeli temeljeni na Markovljevim lancima u neprekidnom vremenu
2022. urn:nbn:hr:126:044768
Kljajić, Kristina
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Kljajić, K. (2022). SIS i SIR epidemiološki modeli temeljeni na Markovljevim lancima u neprekidnom vremenu (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:044768

Kljajić, Kristina. "SIS i SIR epidemiološki modeli temeljeni na Markovljevim lancima u neprekidnom vremenu." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:044768

Kljajić, Kristina. "SIS i SIR epidemiološki modeli temeljeni na Markovljevim lancima u neprekidnom vremenu." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:044768

Kljajić, K. (2022). 'SIS i SIR epidemiološki modeli temeljeni na Markovljevim lancima u neprekidnom vremenu', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 24 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:044768

Kljajić K. SIS i SIR epidemiološki modeli temeljeni na Markovljevim lancima u neprekidnom vremenu [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2022 [cited 2024 December 24] Available at: https://urn.nsk.hr/urn:nbn:hr:126:044768

K. Kljajić, "SIS i SIR epidemiološki modeli temeljeni na Markovljevim lancima u neprekidnom vremenu", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:126:044768

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Metadata
TitleSIS i SIR epidemiološki modeli temeljeni na Markovljevim lancima u neprekidnom vremenu
Title (english)SIS and SIR Epidemiological Continuous - Time Markov Chains
AuthorKristina Kljajić
MentorNenad Šuvak (mentor)
Committee memberIvan Papić (predsjednik povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
Committee memberDanijel Grahovac (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2022-02-22, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
Matematičko modeliranje u epidemiologiji pokušava predvidjet tijek epidemije kako bi pravovremenim donošenjem mjera utjecaj epidemije bio smanjen. Dva osnovna modela su SIS, model koji dijeli populaciju na dvije disjunktne klase jedinki, podložne i zaražene, te ne dopušta stvaranje imuniteta na tu bolest, i SIR, koji uz podložne i zaražene dopušta stvaranje imuniteta stoga postoji treća klasa, oporavljeni. Ti modeli mogu biti promatrani u determinističkom i stohastičkom obliku. U ovom radu opisana je deterministička osnova modela, ali naglasak je bio na stohastičkom obliku, točnije temelj su bili Markovljevi lanci u neprekidnom vremenu. Uz teorijsku podlogu Markovljevih lanaca, svaki model je prikazan deterministički i stohastički, njegova osnovna svojstva i simulacija epidemije bolesti koja spada u taj model.
Abstract (english)
Mathematical modeling in epidemiology predicts the course of an epidemic in order to reduce its impact. Two basic models are SIS, a model that divides the population in two classes, individuals can be susceptible or infected, it does not allow the development of immunity to the disease, and the other one SIR, which allows the development of immunity, so there is a third class of individuals, recovered. These models can be observed in deterministic and stochastic forms. This paper describes the deterministic basis of the model, but the main part is in stochastic form, modeled as Markov chains in a continuous time. In addition to the theoretical basis of Markov chains, each model is presented in deterministic and stochastic form with its basic properties and epidemic simulation.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:044768
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 on2022-02-28 08:19:45