Related papers: Optimized Gillespie algorithms for the simulation …
We present a simple and general framework to simulate statistically correct realizations of a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical an efficient algorithm alike the…
Researchers have employed stochastic simulations to determine the validity of their theoretical findings and to study analytically intractable spreading dynamics. In both cases, the correctness and efficiency of the simulation algorithm are…
Higher-order dynamics refer to mechanisms where collective mutual or synchronous interactions differ fundamentally from their pairwise counterparts through the concept of many-body interactions. Phenomena absent in pairwise models, such as…
Stochastic simulations are one of the cornerstones of the analysis of dynamical processes on complex networks, and are often the only accessible way to explore their behavior. The development of fast algorithms is paramount to allow…
In the infectious disease literature, significant effort has been devoted to studying dynamics at a single scale. For example, compartmental models describing population-level dynamics are often formulated using differential equations. In…
The stochastic simulation algorithm commonly known as Gillespie's algorithm is now used ubiquitously in the modelling of biological processes in which stochastic effects play an important role. In well-mixed scenarios at the sub-cellular…
Models invoking the chemical master equation are used in many areas of science, and, hence, their simulation is of interest to many researchers. The complexity of the problems at hand often requires considerable computational power, so a…
Continuous-time Markov process models of contagions are widely studied, not least because of their utility in predicting the evolution of real-world contagions and in formulating control measures. It is often the case, however, that…
Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…
The Gillespie algorithm provides statistically exact methods for simulating stochastic dynamics modelled as interacting sequences of discrete events including systems of biochemical reactions or earthquake occurrences, networks of queuing…
Rule-based models have been successfully used to represent different aspects of the COVID-19 pandemic, including age, testing, hospitalisation, lockdowns, immunity, infectivity, behaviour, mobility and vaccination of individuals. These…
Discrete stochastic processes are prevalent in natural systems, with applications in physics, biochemistry, epidemiology, sociology, and finance. While analytic solutions often cannot be derived, existing simulation frameworks can generate…
Many physical and biological processes are stochastic in nature. Computational models and simulations of such processes are a mathematical and computational challenge. The basic stochastic simulation algorithm was published by D. Gillespie…
We develop a new methodology for the efficient computation of epidemic final size distributions for a broad class of Markovian models. We exploit a particular representation of the stochastic epidemic process to derive a method which is…
A general formalism is introduced to allow the steady state of non-Markovian processes on networks to be reduced to equivalent Markovian processes on the same substrates. The example of an epidemic spreading process is considered in detail,…
The presence of erratic or unstable paths in standard kinetic Monte Carlo simulations significantly undermines the accurate simulation and sampling of transition pathways. While typically reliable methods, such as the Gillespie algorithm,…
We present a computational modeling framework for data-driven simulations and analysis of infectious disease spread in large populations. For the purpose of efficient simulations, we devise a parallel solution algorithm targeting…
We developed a model and a software package for stochastic simulations of transmission of COVID-19 and other similar infectious diseases, that takes into account contact network structures and geographical distribution of population…
Parameter estimation for discretely observed Markov processes is a challenging problem. However, simulation of Markov processes is straightforward using the Gillespie algorithm. We exploit this ease of simulation to develop an effective…
Many multiagent dynamics, including various collective dynamics occurring on networks, can be modeled as a stochastic process in which the agents in the system change their state over time in interaction with each other. The Gillespie…