A model from from Allen & Dytham (2009) written in Python. The model is used to demonstrate the use of an individual-based, stochastic simulation of biological populations in continuous time.

Two algorithms are coded up from the paper: 1) a novel algorithm from Allen & Dytham (2009), here called the A&D Method; and 2) the Gillespie Alorithm developed in Gillespie (1976, 1979), and otherwise known as the Direct Method. Whilst the A&D Method performs much faster than the Direct Method and converges on the same solution, it appears to generate much noisier outputs around that solution (general observation, not formally tested).

Allen, George Edward, and Calvin Dytham. "An efficient method for stochastic simulation of biological populations in continuous time." Biosystems 98.1 (2009): 37-42.

Gillespie, Daniel T. "A general method for numerically simulating the stochastic time evolution of coupled chemical reactions." Journal of computational physics 22.4 (1976): 403-434.

Gillespie, Daniel T. "Exact stochastic simulation of coupled chemical reactions." The journal of physical chemistry 81.25 (1977): 2340-2361.