Modeling Demographic Noise in Discrete and Continuous Settings

In this paper, we numerically compare two distinct techniques for modeling demographic noise in biomathematical systems: the forward method introduced by Allen, which starts from discrete stochastic processes and moves forward to their continuous counterparts, and the backward technique introduced by Carletti and Banerjee, which models discrete stochastic processes incorporating intrinsic noise by moving backward from ordinary differential equation (ODE) systems. Our work highlights that the two methods show consistent dynamical trends. Nevertheless, the backward technique offers greater ease of use and provides a wider range of applications, as it allows researchers to infer demographic stochasticity directly from systems previously modeled by standard ODEs.