Random variation in model parameters: A comprehensive review of stochastic logistic growth equation

Abstract

Biological growth curves are central to interdisciplinary research that seeks to improve our understanding of natural processes. Applications of growth equations are widespread across domains, with one particular growth equation being the dominant one: the logistic growth model. Nonlinear models that use parameters to vary with time are essential mathematical tools for analyzing growth patterns in different research areas. Recent research has investigated continuous parameter variation and an empirical method of detecting parameter variation has been proposed (Karim et al., 2022). In the literature, instances are abundant where the parameters vary randomly with time. This review article is focused on the stochastic version of the logistic equation, where researchers introduced stochasticity through random variation of one or more parameters in the model. Our survey reports a segmentation of articles based on the logistic growth equations into harvesting and non-harvesting equations and points out some key future study directions that may demand attention from researchers. This study also identifies the need for data-driven research in stochastic growth equations to improve the applicability of these models for real data application.