o:3256 Stohastički epidemiološki modeli i njihova analiza Stochasic epidemiological models and their analysis : doctoral dissertation sr This doctoral dissertation aims to analyze existing epidemiological models, their modifications, and newly defined stochastic models. Stochastic epidemiological models are constructed using deterministic models enriched with multidimensional Brownian motion, Lévy processes, Markov chains, and processes with delay. The appropriate conditions on model parameters under which disease extinction and persistence occur are derived. The techniques applied in the proofs depend on the type of equation considered as well as the assumptions made about its coefficients. Furthermore, both short-term and long-term predictions within the realm of stochastic models are illustrated; these can be applied to the prevention and control of specific diseases. The results are confirmed through examples demonstrating the advantages of the newly introduced models compared to existing ones. Biografija: str. [204-205].Bibliografija: str. [206]. Datum odbrane: 22.10.2025 Stochastic analysis 91552100 186269705 91552101 8822 2026-04-07T17:17:16.053Z 45 no 46 Bojana, 1991- Jovanović 133701641 2025 63 mentor Jasmina S., 1982- Đorđević 15444327 2025 63 član komisije Marija G., 1982- Milošević 15445607 2025 63 član komisije Dušan D., 1991- Đorđević 80075529 2025 63 član komisije Nenad, 1981- Šuvak 133706761 2025 [7], 203 str. 6607689 http://phaidrani.ni.ac.rs/o:3256 no yes 12 2026-04-07T17:17:16.320Z 70 stohastičke diferencijalne jednačine, Braunovo kretanje, vremenski zavisno kašnjenje, proces Levija, proces Markova, iskorenjivanje, perzistentnost u srednjem, stacionarna raspodela stochastic differential equations, Brownian motion, time-dependent delay, Lévy process, Markov process, extinction, persistence in mean, stationary distribution 519.218:616-036.22(043.3) P 001 1738 18A07 18A0701 2025