Title: Study of a birth-death process with population independent death rate

Authors: Mathew P. Sindu; Narayanan C. Viswanath

Addresses: Department of Mathematics, Government Engineering College, Thrissur, Thrissur-680009, Kerala, India ' Department of Mathematics, Government Engineering College, Thrissur, Thrissur-680009, Kerala, India

Abstract: Birth-death processes are extensively used in modelling several real-world phenomena. For example, the widely used exponential growth model is a pure birth model. This paper presents a birth-death process with time-inhomogeneous birth and death rates, where the death rate is independent of the population size. Transient analysis of the process is conducted using the generating function method. Mean, variance, and extinction probability are obtained by solving Volterra integral equations using numerical methods. A comparison, in terms of average, with the deterministic counterpart of the birth-death model shows that the influence of the initial population size separates the averages. A numerical study reveals that the new model outperforms the exponential growth model and could be its substitute in several real-world applications, including tumour growth modelling.

Keywords: birth-death process; transient analysis; Volterra integral equation; deterministic model; exponential growth model.

DOI: 10.1504/IJMOR.2024.138533

International Journal of Mathematics in Operational Research, 2024 Vol.28 No.1, pp.60 - 77

Received: 01 Jul 2022
Accepted: 11 Mar 2023
Published online: 09 May 2024 *

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