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A spatially heterogeneous gillespie algorithm modeling framework that enables individual molecule history and tracking

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2017年 62卷 304-311页

作者： Melunis, Justin Hershberg, Uri Drexel Univ Sch Biomed Engn & Hlth Sci 3141 Chestnut St Philadelphia PA 19104 USA

Stochastic models allow investigators to simulate reactions in a discrete way that can account for fluctuations that are otherwise ignored within a deterministic approach. Integrated particle system (IPS) models are a form of stochastic model that take spatial distributions, environmental factors, and agent migration into consideration. Unlike agent based models (ABM), IPS models only rely on a set of general reactions to describe the interactions of molecules/entities, allowing for an easy cause-effect connection between macroscopic phenomena and microscopic behavior. However, IPS models currently do not track individual agents or apply manipulations to individual agent behavior based on their specific location or their individual history. Therefore, IPS models cannot incorporate agent-based manipulations and tracking while still relying on a set of basic assumptions that are needed to easily connect emergent phenomena to simplistic microscopic behaviors. Here we propose an IPS modeling framework where we convert the exact gillespie algorithm into a 2 dimensional lattice space that allows for environmental factors where molecules can move stochastically, generating an overall heterogeneous molecule distribution. Individual molecules can be tracked without describing the rules of interaction for each specific individual molecule, forming a tracked IPS (TIPS) modeling framework. However, since each individual molecule is tagged, agent-based manipulations and the ability to alter agent behavior due to history can be incorporated into TIPS, allowing one to model biological systems that would otherwise have to rely on a pure ABM. We apply the TIPS modeling framework to STIM1(stromal interaction molecule 1)-Orail(calcium release-activated calcium channel protein 1) binding and motion, in T cells as a result of T cell receptor activation a key component of the calcium response within lymphocytes that leads to the adaptive response of T cells in an immune response. Within

关键词： Integrated Particle System Stochastic Modeling gillespie algorithm Tracking Immunology STIM

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Geospatial model of COVID-19 spreading and vaccination with event gillespie algorithm

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NONLINEAR DYNAMICS 2022年第1期109卷 239-248页

作者： Temerev, Alexander Rozanova, Liudmila Keiser, Olivia Estill, Janne Univ Geneva Inst Global Hlth Geneva Switzerland

We have developed a mathematical model and stochastic numerical simulation for the transmission of COVID-19 and other similar infectious diseases that accounts for the geographic distribution of population density, detailed down to the level of location of individuals, and age-structured contact rates. Our analytical framework includes a surrogate model optimization process to rapidly fit the parameters of the model to the observed epidemic curves for cases, hospitalizations, and deaths. This toolkit (the model, the simulation code, and the optimizer) is a useful tool for policy makers and epidemic response teams, who can use it to forecast epidemic development scenarios in local settings (at the scale of cities to large countries) and design optimal response strategies. The simulation code also enables spatial visualization, where detailed views of epidemic scenarios are displayed directly on maps of population density. The model and simulation also include the vaccination process, which can be tailored to different levels of efficiency and efficacy of different vaccines. We used the developed framework to generate predictions for the spread of COVID-19 in the canton of Geneva, Switzerland, and validated them by comparing the calculated number of cases and recoveries with data from local seroprevalence studies.

关键词： COVID-19 Spatial epidemic modeling gillespie algorithm Contact matrices Population density

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A Massively Parallel Implementation of gillespie algorithm on FPGAs

A Massively Parallel Implementation of Gillespie Algorithm o...

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30th Annual International Conference of the IEEE-Engineering-in-Medicine-and-Biology-Society

作者： Macchiarulo, Luca Univ Hawaii Manoa Dept Elect Engn Honolulu HI 96822 USA

ISBN: (纸本)9781424418145

This paper targets the acceleration of complex stochastic simulations of biochemical systems by a dedicated hardware architecture on configurable devices (FPGA). Existing approaches are discussed and compared with the proposed one, and experimental data is introduced to support the feasibility of the system. Retargetable hardware description can be automatically generated for any suitable simulation problem, and preliminary results show very high performance - 100 million time steps per second for large models (1000 reactions).

关键词： Monte Carlo Simulation gillespie algorithm Field Programmable Gate Arrays

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Continuous time boolean modeling for biological signaling: application of gillespie algorithm

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BMC SYSTEMS BIOLOGY 2012年第1期6卷 116-116页

作者： Stoll, Gautier Viara, Eric Barillot, Emmanuel Calzone, Laurence Inst Curie F-75248 Paris France INSERM U900 F-75248 Paris France Mines ParisTech F-77300 Fontainebleau France Sysra F-91330 Yerres France

Mathematical modeling is used as a Systems Biology tool to answer biological questions, and more precisely, to validate a network that describes biological observations and predict the effect of perturbations. This article presents an algorithm for modeling biological networks in a discrete framework with continuous time. Background: There exist two major types of mathematical modeling approaches: (1) quantitative modeling, representing various chemical species concentrations by real numbers, mainly based on differential equations and chemical kinetics formalism;(2) and qualitative modeling, representing chemical species concentrations or activities by a finite set of discrete values. Both approaches answer particular (and often different) biological questions. Qualitative modeling approach permits a simple and less detailed description of the biological systems, efficiently describes stable state identification but remains inconvenient in describing the transient kinetics leading to these states. In this context, time is represented by discrete steps. Quantitative modeling, on the other hand, can describe more accurately the dynamical behavior of biological processes as it follows the evolution of concentration or activities of chemical species as a function of time, but requires an important amount of information on the parameters difficult to find in the literature. Results: Here, we propose a modeling framework based on a qualitative approach that is intrinsically continuous in time. The algorithm presented in this article fills the gap between qualitative and quantitative modeling. It is based on continuous time Markov process applied on a Boolean state space. In order to describe the temporal evolution of the biological process we wish to model, we explicitly specify the transition rates for each node. For that purpose, we built a language that can be seen as a generalization of Boolean equations. Mathematically, this approach can be translated in a set of ord

关键词： Boolean modeling Continuous time Markov process gillespie algorithm

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The Application of gillespie algorithm in Spreading

The Application of Gillespie Algorithm in Spreading

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3rd International Conference on Mechatronics Engineering and Information Technology(ICMEIT 2019)

作者： Xiaomin Deng Xiaomeng Wang College of computer and information science Southwest University

The contagion models of disease-spread which predict the epidemics grow with time goes by have been widely researched in social networks. The discrete-time simulation method, Monte Carlo Simulation where time is discretized into uniform steps and transition rates between states are replaced by transition probabilities, are mostly applied when simulating the models. In this paper, we propose a continuous-time approach, the gillespie algorithm, which can be used for fast simulation of stochastic processes, is event-driven rather than using equally-spaced time steps. We show how the method can be adapted to the epidemic models, mainly in the susceptible-infected model and susceptible-infected-susceptible model, and confirm the accuracy of the method with numerical simulations. Based on the accuracy of the method, we make some changes in epidemic models to make the models more applicable.

关键词： contagion model epidemic discrete-time continuous-time gillespie algorithm

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A gillespie-Type algorithm for Particle Based Stochastic Model on Lattice

A Gillespie-Type Algorithm for Particle Based Stochastic Mod...

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作者： Liu, Weigang Virginia Tech | University

In this thesis, I propose a general stochastic simulation algorithm for particle based lattice model using the concepts of gillespie’s stochastic simulation algorithm, which was originally designed for well-stirred systems. I describe the details about this method and analyze its complexity compared with the StochSim algorithm, another simulation algorithm originally proposed to simulate stochastic lattice model. I compare the performance of both algorithms with application to two different examples: the May-Leonard model and Ziff-Gulari-Barshad model. Comparison between the simulation results from both algorithms has validate our claim that our new proposed algorithm is comparable to the StochSim in simulation accuracy. I also compare the efficiency of both algorithms using the CPU cost of each code and conclude that the new algorithm is as efficient as the StochSim in most test cases, while performing even better for certain specific cases.

关键词： gillespie algorithm stochastic simulation lattice model Thesis

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Optimized gillespie algorithms for the simulation of Markovian epidemic processes on large and heterogeneous networks

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COMPUTER PHYSICS COMMUNICATIONS 2017年 219卷 303-312页

作者： Cota, Wesley Ferreira, Silvio C. Univ Fed Vicosa Dept Fis BR-36570000 Vicosa MG Brazil

Numerical simulation of continuous-time Markovian processes is an essential and widely applied tool in the investigation of epidemic spreading on complex networks. Due to the high heterogeneity of the connectivity structure through which epidemic is transmitted, efficient and accurate implementations of generic epidemic processes are not trivial and deviations from statistically exact prescriptions can lead to uncontrolled biases. Based on the gillespie algorithm (GA), in which only steps that change the state are considered, we develop numerical recipes and describe their computer implementations for statistically exact and computationally efficient simulations of generic Markovian epidemic processes aiming at highly heterogeneous and large networks. The central point of the recipes investigated here is to include phantom processes, that do not change the states but do count for time increments. We compare the efficiencies for the susceptible infected susceptible, contact process and susceptible infected recovered models, that are particular cases of a generic model considered here. We numerically confirm that the simulation outcomes of the optimized algorithms are statistically indistinguishable from the original GA and can be several orders of magnitude more efficient. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Complex networks Markovian epidemic processes gillespie algorithm

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On the use of gillespie stochastic simulation algorithm in a model of the human immune system response to the Yellow Fever vaccine

On the use of Gillespie stochastic simulation algorithm in a...

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Biological Ontologies and Knowledge Bases Workshop at IEEE International Conference on Bioinformatics and Biomedicine (IEEE BIBM)

作者： Xavier, M. P. Bonin, C. R. B. dos Santos, R. W. Lobosco, M. Univ Fed Juiz de Fora Grad Program Computat Modeling BR-36036900 Juiz De Fora MG Brazil

ISBN: (纸本)9781509030507

The Human Immune System (HIS) plays a fundamental role in the defense of the body against diseases. However, the multi-scale interactions among several of its components make the complete understanding of the mechanisms involved in the body defense a complex task. Mathematical and computational tools can help towards this goal. Lots of works use differential equations, agent-based models and cellular automaton to describe the behavior of the HIS. In this work, we use the gillespie stochastic simulation algorithm to model the stochastic nature of the HIS response to Yellow Fever vaccine.

关键词： Mathematical modeling Computational modeling Immune System gillespie algorithm Modeling techniques

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Mathematical Modeling and Simulation of Logistic Growth

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APPLIED SCIENCES-BASEL 2025年第8期15卷 4409-4409页

作者： Pelagalli, Camilla Faccio, Stefano Casari, Paolo Univ Trento Dept Informat Engn & Comp Sci I-38123 Trento Italy

We propose a reproducible pipeline of work consisting of the time-driven simulation of discrete logistic growth based on the corresponding master equation, focusing on demographic variation under a carrying capacity limit. The mathematical modeling that leads to the stochastic implementation is presented in a step-by-step fashion to statistically ground the designed simulation. The main parameters of the system, whose settings include extreme values, are varied to analyze the simulation behavior and explore the empirical limits of its applicability, minimizing the distance between the theoretical and observed carrying capacity trough parameter tuning. After such tuning, a single simulation scenario is chosen and compared with the state-of-the-art gillespie algorithm, which adopts a contrasting event-driven approach. The output analysis of these two strategies and the assessment of their statistical significance highlight the trade-off between adherence to the model and the computational effort of the proposed approach, while shedding light on multiple facets of logistic growth, including discrepancies between continuous and discrete models.

关键词： logistic growth population ecology continuous vs. discrete time deterministic vs. stochastic model gillespie algorithm parameter tuning analysis of residuals

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Recent advances in stochastic simulation algorithms create opportunities to study new ecological and eco-evolutionary problems

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OIKOS 2025年第1期2025卷

作者： Kummel, Misha T. Vasseur, David A. Yale Univ Dept Ecol & Evolutionary Biol New Haven CT 06520 USA

Incorporating stochasticity into ecological modeling is vital for understanding the structure and function of ecological systems, but stochasticity has been challenging to consistently introduce into foundational ecological theory. The gillespie stochastic simulation algorithm (herein SSA) provides a key method to represent demographic stochasticity, but due to its foundational assumptions is inadequate for problems involving intra-population variation and extrinsically/environmentally-driven rapid changes in demographic rates. Two recent extensions to the SSA address these limitations: one augments the SSA with individual-linked trait distributions that let us track trait changes across individuals and populations and the other introduces a methodological innovation to allow demographic rates to change between events;in four case studies we demonstrate the utility of these advances and highlight that simultaneously integrating both extensions into a single framework allows us to tackle a new class of ecological and evolutionary questions that have typically not been explored in continuous time modeling.

关键词： demographic stochasticity environmental change gillespie algorithm stochastic simulation trait variation

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