On a stochastic logistic population model with time-varying carrying capacity

Abstract

In this paper, we deal with the logistic growth model with a time-dependent carrying capacity that was proposed in the literature for the study of the total bacterial biomass during occlusion of healthy human skin. Accounting for data and model errors, randomness is incorporated into the equation by assuming that the input parameters are random variables. The uncertainty is quantified by approximations of the solution stochastic process via truncated series solution together with the random variable transformation method. Numerical examples illustrate the theoretical results.