Stochasic epidemiological models and their analysis

[B. Lj. Jovanović]

[7], 203 str.

Biografija: str. [204-205]. Bibliografija: str. [206].

Stochastic analysis

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.

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

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