On the numerical analysis of stochastic Lotka-Volterra models

The stochastic Lotka-Volterra model is an infinite Markov population model that has applications in various life science domains. Its analysis is challenging since, besides an infinite state space with unbounded rates, it shows strongly fluctuating dynamics and becomes unstable in the long-run. Traditional numerical methods are therefore not appropriate to solve the system. Here, we suggest adaptations and combinations of traditional methods that yield fast and accurate solutions for certain parameter ranges of the stochastic Lotka-Volterra model. We substantiate our theoretical investigations with a comparison based on experimental results.