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

Abstract

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

Stochastic models for phytoplankton dynamics in Mediterranean Sea

“…(1)- (7) within the Ito scheme, and averaging over 1000 realizations (Spagnolo et al, 2004;Giuffrida et al, 2009;Denaro et al, 2013a,b). The numerical method, whose computer implementation consists in a C++ program, is based on an explicit finite difference scheme with centered-in-space differencing for the diffusion term and forward differencing for the advection term.…”

Spatio-temporal behaviour of the deep chlorophyll maximum in Mediterranean Sea: Development of a stochastic model for picophytoplankton dynamics

“…Therefore, one cannot expect that the presence of a symmetric noise with zero mean, i.e. Gaussian noise used in the model, produces in average the same effect as a deterministic dynamics (Giuffrida et al, 2009). On the other side, the use of a random function, i.e.…”

Stability in a system subject to noise with regulated periodicity

“…Specifically, random variations of species concentrations in natural ecosystems [1,2,[11][12][13], the role of molecular noise in the growth of bacteria that are present in food products [14], and the stochastic dynamics of diseases connected with genetic mutations [15] are fundamental aspects that cannot be neglected when seeking a better understanding of the dynamics of complex living systems. In particular, in these systems the random variations of temperature, food resources, and other environmental parameters can be described using models in which multiplicative noise sources are present [8,16,17].…”