In numerically simulating the time evolution of a well-stirred chemically reacting system, the recently introduced “tau-leaping” procedure attempts to accelerate the exact stochastic simulation algorithm by using a special Poisson approximation to leap over sequences of non-critical reaction events. Presented here is an improved procedure for determining the maximum leap size for a specified de...

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuo...

Starting with stochastic rate equations for the fundamental interactions between microbes and their viruses, we derive a mean-field theory for the population dynamics of microbe-virus systems, including the effects of lysogeny. In the absence of lysogeny, our model is a generalization of that proposed phenomenologically by Weitz and Dushoff. In the presence of lysogeny, we analyze the possible ...

The threat of invasive species has increased with the expansion of global transportation. In the United States, zebra mussels became a problem by the early 1990’s when they were introduced by ballast water into Lake St. Clair in 1988. In 2007, a new deterministic discrete-time model for zebra mussel populations was proposed by Casagrandi. We show how this model produces periodic, stable, and ch...

We present a study of the spatial correlation functions of a one-dimensional reaction-diffusion system in both equilibrium and out of equilibrium. For the numerical simulations we have employed the Gillespie algorithm dividing the system in cells to treat diffusion as a chemical process between adjacent cells. We find that the spatial correlations are spatially short ranged in equilibrium but b...

Summary SIApopr (Simulating Infinite-Allele populations) is an R package to simulate time-homogeneous and inhomogeneous stochastic branching processes under a very flexible set of assumptions using the speed of C ++. The software simulates clonal evolution with the emergence of driver and passenger mutations under the infinite-allele assumption. The software is an application of the Gillespie S...

The Gillespie τ-Leaping Method is an approximate algorithm that is faster than the exact Direct Method (DM) due to the progression of the simulation with larger time steps. However, the procedure to compute the time leap τ is quite expensive. In this paper, we explore the acceleration of the τ-Leaping Method using Graphics Processing Unit (GPUs) for ultra-large networks (>0.5e(6) reaction chann...

We introduce a minimal model description for the dynamics of transcriptional regulatory networks. It is studied within a mean-field approximation, i.e., by deterministic ode's representing the reaction kinetics, and by stochastic simulations employing the Gillespie algorithm. We elucidate the different results both approaches can deliver, depending on the network under study, and in particular ...

In this paper we show some applications of Advanced and Parallel Computing to the study of mathematical models in Systems Biology and in particular of the networks of biochemical reactions occurring inside a cell. Due to their high complexity, the numerical study of these systems must be approached by means of sophisticated Advanced Computing tools. Two examples are shown: in a deterministic fr...

Parasites play a central role in tropical ecosystems, affecting the ecology and evolution of species interactions, host population growth and regulation, and community biodiversity (Esch and Fernandez 1993; Hudson, Dobson and Newborn 1998; Hochachka and Dhondt 2000; Hudson et al. 2002). Our understanding of how natural and anthropogenic factors affect host-parasite dynamics in free-ranging prim...