A note on the logistic equation subject to uncertainties in parameters

Abstract

This paper discusses the logistic equation subject to uncertainties in the intrinsic growth rate, $\alpha$, in the initial population density, $N_0$, and in the environmental carrying capacity, K. These parameters are treated as independent random variables. The random variable transformation method is applied to compute the first probability density function of the time–population density, N(t), and of its inflection point, $t^{*}$. Results for the density functions of N(t), for a fixed $t>0$, and $t^{*}$ are also provided for $\alpha$, $N_0$ and K uniformly distributed. Finally, numerical experiments illustrate the proposed theoretical results.