Time-Inhomogeneous Finite Birth Processes with Applications in Epidemic Models

We consider the evolution of a finite population constituted by susceptible and infectious individuals and compare several time-inhomogeneous deterministic models with their stochastic counterpart based on finite birth processes. For these processes, we determine the explicit expressions of the tran...

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Veröffentlicht in:Mathematics (Basel) 2023-11, Vol.11 (21), p.4521
Hauptverfasser: Giorno, Virginia, Nobile, Amelia G
Format: Artikel
Sprache:eng
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Zusammenfassung:We consider the evolution of a finite population constituted by susceptible and infectious individuals and compare several time-inhomogeneous deterministic models with their stochastic counterpart based on finite birth processes. For these processes, we determine the explicit expressions of the transition probabilities and of the first-passage time densities. For time-homogeneous finite birth processes, the behavior of the mean and the variance of the first-passage time density is also analyzed. Moreover, the approximate duration until the entire population is infected is obtained for a large population size.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11214521