This paper concerns numerical comparisons between five mathematical models capable of modelling the stochastic behaviour of
neutrons in low extraneous (extrinsic or fixed) neutron source applications. These models include analog Monte-Carlo (AMC),
forward probability balance equations (FPB), generating function form of the forward probability balance equations (FGF), generating
function form of the backward probability balance equations (P´al-Bell), and an Itˆo calculus model using both an explicit and
implicit Euler-Maruyama discretization scheme. Results such as the survival probability, extinction probability, neutron population
mean and standard deviation, and neutron population cumulative distribution function have all been compared. The least computationally
demanding mathematical model has been found to be the use of the P´al-Bell equations which on average take four orders
of magnitude less time to compute than the other methods in this study. The accuracy of the AMC and FPB models have been
found to be strongly linked to the computational e ciency of the models. The computational e ciency of the models decrease
significantly as the maximum allowable neutron population is approached. The Itˆo calculus methods, utilising explicit and implicit
Euler-Maruyama discretization schemes, have been found to be unsuitable for modelling very low neutron populations. However,
improved results, using the Itˆo calculus methods, have been achieved for systems containing a greater number of neutrons.