Time-Inhomogeneous Finite Birth Processes with Applications in Epidemic Models

Virginia Giorno and Amelia G. Nobile ()
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Virginia Giorno: Dipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano, Salerno, Italy
Amelia G. Nobile: Dipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano, Salerno, Italy

Mathematics, 2023, vol. 11, issue 21, 1-31

Abstract: 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.

Keywords: population growth models; probability distribution of the number of infections; duration of the epidemic; first-passage time density; asymptotic behaviors (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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