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Time-Inhomogeneous Finite Birth Processes with Applications in Epidemic Models

Author

Listed:
  • Virginia Giorno

    (Dipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano, Salerno, Italy
    These authors contributed equally to this work.)

  • Amelia G. Nobile

    (Dipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano, Salerno, Italy
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Virginia Giorno & Amelia G. Nobile, 2023. "Time-Inhomogeneous Finite Birth Processes with Applications in Epidemic Models," Mathematics, MDPI, vol. 11(21), pages 1-31, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4521-:d:1272972
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    References listed on IDEAS

    as
    1. Giorno, Virginia & Nobile, Amelia G., 2022. "On some integral equations for the evaluation of first-passage-time densities of time-inhomogeneous birth-death processes," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    2. M. J. Faddy & J. S. Fenlon, 1999. "Stochastic modelling of the invasion process of nematodes in fly larvae," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(1), pages 31-37.
    Full references (including those not matched with items on IDEAS)

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