Title: A stochastic extension of the T growth model
Authors: Antonio Barrera - Universidad de Malaga (Spain) [presenting]
Patricia Roman-Roman - Universidad de Granada (Spain)
Francisco Torres-Ruiz - University of Granada (Spain)
Abstract: Stochastic growth models are of great importance due to the ability to include random influences produced by internal and external conditions. Usually, these models are extensions of deterministic models related with growth curves such as the classical logistic, Weibull or, more recently, hyperbolastic. One of the most interesting recent curves is the one associated with the $T$ model, which has become useful in modelling bacterial growth or proliferation and regression of cancer cells. This deterministic model is able to represent sigmoidal and biphasic growth with great accuracy, but it does not take into account random effects. A stochastic extension based on the $T$ model is proposed. Starting from a parametric modification of the original curve, a time nonhomogeneous diffusion process is built providing the same mean behaviour. The main issue is related with the estimation of the parameters, because of the complexity of the model. In order to deal with this problem, different strategies based on the reformulation of maximum likelihood equations and the use of metaheuristic algorithms, are considered. Finally, usefulness of the stochastic model is illustrated by performing some practical applications.