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

Mathew P. Sindu and Narayanan C. Viswanath

International Journal of Mathematics in Operational Research, 2024, vol. 28, issue 1, 60-77

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. (search for similar items in EconPapers)
Date: 2024
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