A stochastic interspecific competition model to predict the behaviour of Listeria monocytogenes in the fermentation process of a traditional Sicilian salami

The present article discusses the use of modified Lotka-Volterra equations in order to stochastically simulate the behaviour of Listeria monocytogenes and lactic acid bacteria (LAB) during the fermentation period (168 h) of a typical Sicilian salami. For this purpose, the differential equation system is set considering temperature (T), pH, water activity (aw) as stochastic variables. Each of them is governed by dynamics that involve a deterministic linear decrease as a function of the time t and an additive noise term which instantaneously mimics the fluctuations of T, pH and aw. The choice of a suitable parameter accounting for the interaction of LAB on L. monocytogenes as well as the introduction of appropriate noise levels allows to match the observed data, both for the mean growth curves and for the probability distribution of L. monocytogenes concentration at 168 h.