Simulation Of Stochastic Networks Research Articles

Simulation of Full HIV Cluster Networks in a Nationally Representative Model Indicates Intervention Opportunities.

Clusters of rapid HIV transmission in the United States are increasingly recognized through analysis of HIV molecular sequence data reported to the National HIV Surveillance System. Understanding the full extent of cluster networks is important to assess intervention opportunities. However, full cluster networks include undiagnosed and other infections that cannot be systematically observed in real life. We replicated HIV molecular cluster networks during 2015-2017 in the United States using a stochastic dynamic network simulation model of sexual transmission of HIV. Clusters were defined at the 0.5% genetic distance threshold. Ongoing priority clusters had growth of ≥3 diagnoses/year in multiple years; new priority clusters first had ≥3 diagnoses/year in 2017. We assessed the full extent, composition, and transmission rates of new and ongoing priority clusters. Full clusters were 3-9 times larger than detected clusters, with median detected cluster sizes in new and ongoing priority clusters of 4 (range 3-9) and 11 (range 3-33), respectively, corresponding to full cluster sizes with a median of 14 (3-74) and 94 (7-318), respectively. A median of 36.3% (range 11.1%-72.6%) of infections in the full new priority clusters were undiagnosed. HIV transmission rates in these clusters were >4 times the overall rate observed in the entire simulation. Priority clusters reflect networks with rapid HIV transmission. The substantially larger full extent of these clusters, high proportion of undiagnosed infections, and high transmission rates indicate opportunities for public health intervention and impact.

Experimental evaluation of a machine learning approach to improve the reproducibility of network simulations

A stochastic network simulation is verified when its distribution of outputs is aligned with the ground truth, while tolerating deviations due to variability in real-world measurements and the randomness of a stochastic simulation. However, comparing distributions may yield false positives, as erroneous simulations may have the expected distribution yet present aberrations in low-level patterns. For instance, the number of sick individuals may present the right trend over time, but the wrong individuals were infected. We previously proposed an approach that transforms simulation traces into images verified by machine learning algorithms that account for low-level patterns. We demonstrated the viability of this approach when many simulation traces are compared with a large ground truth data set. However, ground truth data are often limited. For example, a publication may include few images of their simulation as illustrations; hence, teams that independently re-implement the model can only compare low-level patterns with few cases. In this paper, we examine whether our approach can be utilized with very small data sets (e.g., 5–10 images), as provided in publications. Depending on the network simulation model (e.g., rumor spread, cascading failure, and disease spread), we show that results obtained with little data can even surpass results obtained with moderate amounts of data at the cost of variability. Although a good accuracy is obtained in detecting several forms of errors, this paper is only a first step in the use of this technique for verification; hence, future works should assess the applicability of our approach to other types of network simulations.

Global stability and optimal control of epidemics in heterogeneously structured populations exhibiting adaptive behavior

We present a novel SIRS model on scale-free networks that takes into account behavioral memory and time delay to depict an adaptive behavioral feedback mechanism, which can better characterize the actual spread of epidemics. We conduct rigorous analysis on the dynamics of the model, including the basic reproduction number R0, uniform persistence and the global asymptotic stability of equilibria. The model has the sharp threshold property, namely, if R0 is less than 1 then the disease-free equilibrium is globally asymptotically stable while if R0 is larger than 1 then the endemic equilibrium is globally asymptotically stable. We further perform an optimal control study for the model to seek effective vaccination and treatment strategies. The existence and uniqueness of these optimal control strategies are demonstrated. Finally, we perform some stochastic network simulations that yield quantitative agreement with the deterministic mean-field approach. Our findings indicate that time delay does not affect R0, but behavioral memory does.

In-Situ Block Characterization of Jointed Rock Exposures Based on a 3D Point Cloud Model

The importance of in-situ rock block characterization has been realized for decades in rock mechanics and engineering, yet how to reliably measure and characterize the geometrical properties of blocks in varied forms of exposures and patterns of jointing is still a challenging task. Using a point cloud model (PCM) of rock exposures generated from remote sensing techniques, we developed a consistent and comprehensive method for rock block characterization that is composed of two different procedures and a block indicator system. A semi-automatic procedure towards the robust extraction of in-situ rock blocks created by the deterministic discontinuity network on rock exposures (PCM-DDN) was developed. A 3D stochastic discrete fracture network (DFN) simulation (PCM-SDS) procedure was built based on the statistically valid representation of the discontinuity network geometry. A multi-dimensional block indicator system, i.e., the block size, shape, orientation, and spatial distribution pattern for systematic and objective block characterization, was then established. The developed method was applied to a synthetic model of cardboard boxes and three different rock engineering scenarios, including a road cut slope from Spain and two open-pit mining slopes from China. Compared with existing empirical methods, the proposed procedures and the block indicator system are dependable and practically feasible, which can help enhance our understanding of block geometry characteristics in related applications.

Efficient Steady-State Simulation of High-Dimensional Stochastic Networks

We propose and study an asymptotically optimal Monte Carlo estimator for steady-state expectations of a d-dimensional reflected Brownian motion (RBM). Our estimator is asymptotically optimal in the sense that it requires [Formula: see text] (up to logarithmic factors in d) independent and identically distributed scalar Gaussian random variables in order to output an estimate with a controlled error. Our construction is based on the analysis of a suitable multilevel Monte Carlo strategy which, we believe, can be applied widely. This is the first algorithm with linear complexity (under suitable regularity conditions) for a steady-state estimation of RBM as the dimension increases.

HEALTHCARE CRITICAL INFRASTRUCTURE STOCHASTIC INTERDEPENDENCIES SIMULATION MODEL FOR SMART CITIES: FLOOD DISASTER SCENARIO

Abstract. Healthcare Critical Infrastructure (HCI) is not an independent network; the operation of a healthcare facility depends on many other Critical Infrastructure (CI) networks such as electric supply CI, water supply CI, etc., forming an interdependent CI network. During a flooding disaster event, as the flood levels rise, the interdependent HCI network becomes vulnerable. A failure in one of the CI results in failure of the dependent CI. During a disaster event such as flooding, the failures propagate and cause cascading failures like a domino effect. The paper proposes an IoT based flood sensor network integrated with a stochastic Petri net interdependent healthcare critical infrastructure network simulation model. An IoT (Internet of Things) based flood water level sensor network can deliver real-time information on the flood conditions at the various interdependent CI facilities in the interdependent network, using the Sensor Observation Services (SOS). The Stochastic Petri Net (SCPN) based interdependent Healthcare Critical Infrastructure (HCI) simulation model, is used to model and simulate the stochastic interdependencies between the interdependent HCI networks. The real-time flood sensor network is integrated with the SCPN based interdependent HCI simulation model. The end to end system is developed in a spatiotemporal environment. This kind of an integrated simulation model will help the end-user to understand system dynamics in real-time, visualize and predict the propagation of cascading failure scenarios in an Interdependent HCI network in a spatiotemporal environment, during a flooding scenario. Real-time information simulation would help disaster response personnel to respond to the question, ‘what if something else happens?

Global Stability of Epidemic Models With Imperfect Vaccination and Quarantine on Scale-Free Networks

Public health services are constantly searching for ways to reduce the spread of infectious diseases, such as public vaccination of asymptomatic individuals, quarantine and treatment of symptomatic individuals. In this paper, we introduce epidemic models including variable population size, degree-related imperfect vaccination and quarantine on scale-free networks. More specifically, the models are formulated both on the population with and without permanent natural immunity to infection, which corresponds respectively to the susceptible-vaccinated-infected-quarantined-recovered (SVIQR) model and the susceptible-vaccinated-infected-quarantined (SVIQS) model. We develop different mathematical methods to study the dynamics of two models, including the basic reproduction number, the global stability of disease-free and endemic equilibria. For the SVIQR model, we show that the system exhibits a forward bifurcation. Meanwhile, the disease-free and unique endemic equilibria are shown to be globally asymptotically stable by constructing suitable Lyapunov functions. For the SVIQS model, conditions ensuring the occurrence of multiple endemic equilibria are derived. Under certain conditions, this system cannot undergo a backward bifurcation. The global asymptotical stability of disease-free equilibrium, and the persistence of the disease are proved. The endemic equilibrium is shown to be globally attractive by using monotone iterative technique. Finally, stochastic network simulations yield quantitative agreement with the deterministic mean-field approach.

Simulations Studies of Protein Kinases that are Molecular Targets in Cancer

AbstractProtein kinases are enzymes with partially overlapping specificities, many of which are important clinical targets. In this article, we give some background on protein kinases and discuss in more depth four such enzymes that have been studied in our labs using computer simulations. The combination of molecular dynamics simulations and enzyme or cell growth experiments was instrumental to explain why certain mutations lead (or do not lead) to resistance to targeted therapy aimed at these proteins. Stochastic network simulations were used to study protein‐protein interactions and suggest points for intervention against tumour growth.

Application of stochastic joint network simulation to composite strata of shallow-buried long-span metro tunnels

A large number of shallow-buried tunnels have currently been built in cities, and specific strata, such as thick upper-soft and lower-hard ground layers, are often encountered. For shallow-buried large-span metro tunnels in urban composite strata, it is particularly important to study the effects of rock mass structures on engineering applications; random joint network simulation technology is a suitable method to study this problem. Considering the shallow-buried large-span metro tunnel in Dalian, which is located in a composite stratum, as the engineering background, first, a set of visualizations is developed with a joint network simulation program. The program can also generate several sets of joints and multistratum random joint networks and then combine program-generated data files and UDEC discrete element software-generated random network models. Combined with orthogonal testing, the failure modes of shallow-buried large-span metro tunnels are discussed, and the influences of rock mass structural parameters on tunnel failures are analyzed. The results indicate that the failure modes of all models are shear or tension failure of the overburden strata along weak planes of random joints, which eventually leads to the occurrence of staggered traction slip collapses and clear slip surfaces. This study provides a certain degree of guidance for the deformation and failure of shallow-buried large-span metro tunnels and for the determination of the surrounding rock pressure in urban composite strata.

Basin entropy behavior in a cyclic model of the rock-paper-scissors type

We deal with stochastic network simulations in a model with three distinct species that compete under cyclic rules which are similar to the rules of the popular rock-paper-scissors game. We investigate the Hamming distance density and then the basin entropy behavior, running the simulations for some typical values of the parameters mobility, predation and reproduction and for very long time evolutions. The results show that the basin entropy is another interesting tool of current interest to investigate chaotic features of the network simulations that are usually considered to describe aspects of biodiversity in the cyclic three-species model.

Reliability Analysis of Rock Slope Excavation Considering the Stochasticity and Finite Persistence of Wedges

With a focus on wedge failure during rock slope excavation and considering stochasticity and finite persistence based on a stochastic structural-plane network simulation and Lajtai’s rock resistance criteria, we present a simplified method combined with binary particle swarm optimization (BPSO) to calculate the shear strength of 3D rock masses. The probabilities of rock slope failure under excavation surfaces of various sizes were obtained using the Monte Carlo method. These probabilities can provide a theoretical basis for determining excavation stability. The approach was applied to a rock slope excavation project in Chongqing, China, and yielded satisfactory results.

Pairwise approximation for SIR-type network epidemics with non-Markovian recovery.

We present the generalized mean-field and pairwise models for non-Markovian epidemics on networks with arbitrary recovery time distributions. First we consider a hyperbolic partial differential equation (PDE) system, where the population of infective nodes and links are structured by age since infection. We show that the PDE system can be reduced to a system of integro-differential equations, which is analysed analytically and numerically. We investigate the asymptotic behaviour of the generalized model and provide an implicit analytical expression involving the final epidemic size and pairwise reproduction number. As an illustration of the applicability of the general model, we recover known results for the exponentially distributed and fixed recovery time cases. For gamma- and uniformly distributed infectious periods, new pairwise models are derived. Theoretical findings are confirmed by comparing results from the new pairwise model and explicit stochastic network simulation. A major benefit of the generalized pairwise model lies in approximating the time evolution of the epidemic.

Efficient simulation of stochastic gene regulatory networks

Gene expression is inherently stochastic, and the dynamics of gene regulatory networks (GRNs) is governed by the Chemical Master Equation (CME). In most cases, the solution of the CME is not available, and the stochastic simulation algorithm (SSA) requires a high computational effort. In this work we illustrate the performance of a method recently developed for the simulation of stochastic gene regulatory networks that allows computational speeds up to 6500 times higher than SSA. Exploiting intrinsic structural properties of GRNs, the method accurately approximates the Chemical Master Equation (CME) with a Partial Integral Differential Equation (PIDE), which is solved numerically by means of a semi-lagrangian method. The method is available within the toolbox SELANSI https://sites.google.com/view/selansi.

SELANSI: a toolbox for simulation of stochastic gene regulatory networks.

MotivationGene regulation is inherently stochastic. In many applications concerning Systems and Synthetic Biology such as the reverse engineering and the de novo design of genetic circuits, stochastic effects (yet potentially crucial) are often neglected due to the high computational cost of stochastic simulations. With advances in these fields there is an increasing need of tools providing accurate approximations of the stochastic dynamics of gene regulatory networks (GRNs) with reduced computational effort.ResultsThis work presents SELANSI (SEmi-LAgrangian SImulation of GRNs), a software toolbox for the simulation of stochastic multidimensional gene regulatory networks. SELANSI exploits intrinsic structural properties of gene regulatory networks to accurately approximate the corresponding Chemical Master Equation with a partial integral differential equation that is solved by a semi-lagrangian method with high efficiency. Networks under consideration might involve multiple genes with self and cross regulations, in which genes can be regulated by different transcription factors. Moreover, the validity of the method is not restricted to a particular type of kinetics. The tool offers total flexibility regarding network topology, kinetics and parameterization, as well as simulation options.Availability and implementationSELANSI runs under the MATLAB environment, and is available under GPLv3 license at https://sites.google.com/view/selansi.

The Effect of Contact Investigations and Public Health Interventions in the Control and Prevention of Measles Transmission: A Simulation Study.

BackgroundMeasles cases continue to occur despite its elimination status in the United States. To control transmission, public health officials confirm the measles diagnosis, identify close contacts of infectious cases, deliver public health interventions (i.e., post-exposure prophylaxis) among those who are eligible, and follow-up with the close contacts to determine overall health outcomes. A stochastic network simulation of measles contact tracing was conducted using existing agent-based modeling software and a synthetic population with high levels of immunity in order to estimate the impact of different interventions in controlling measles transmission.Methods and FindingsThe synthetic population was created to simulate California`s population in terms of population demographics, household, workplace, school, and neighborhood characteristics using California Department of Finance 2010 census data. Parameters for the model were obtained from a review of the literature, California measles case surveillance data, and expert opinion. Eight different scenarios defined by the use of three different public health interventions were evaluated: (a) post-exposure measles, mumps, and rubella (MMR) vaccine, (b) post-exposure immune globulin (IG), and (c) voluntary isolation and home quarantine in the presence or absence of public health response delays. Voluntary isolation and home quarantine coupled with one or two other interventions had the greatest reduction in the number of secondary cases infected by the index case and the probability of escape situations (i.e., the outbreak continues after 90 days).ConclusionsInterrupting contact patterns via voluntary isolation and home quarantine are particularly important in reducing the number of secondary cases infected by the index case and the probability of uncontrolled outbreaks.

Epidemic spreading on adaptively weighted scale-free networks.

We introduce three modified SIS models on scale-free networks that take into account variable population size, nonlinear infectivity, adaptive weights, behavior inertia and time delay, so as to better characterize the actual spread of epidemics. We develop new mathematical methods and techniques to study the dynamics of the models, including the basic reproduction number, and the global asymptotic stability of the disease-free and endemic equilibria. We show the disease-free equilibrium cannot undergo a Hopf bifurcation. We further analyze the effects of local information of diseases and various immunization schemes on epidemic dynamics. We also perform some stochastic network simulations which yield quantitative agreement with the deterministic mean-field approach.

A Multilevel Adaptive Reaction-splitting Simulation Method for Stochastic Reaction Networks

In this work, we present a novel multilevel Monte Carlo method for kinetic simulation of stochastic reaction networks characterized by having simultaneously fast and slow reaction channels. To produce efficient simulations, our method adaptively classifies the reactions channels into fast and slow channels. To this end, we first introduce a state-dependent quantity named level of activity of a reaction channel. Then, we propose a low-cost heuristic that allows us to adaptively split the set of reaction channels into two subsets characterized by either a high or a low level of activity. Based on a time-splitting technique, the increments associated with high-activity channels are simulated using the tau-leap method, while those associated with low-activity channels are simulated using an exact method. This path simulation technique is amenable for coupled path generation and a corresponding multilevel Monte Carlo algorithm. To estimate expected values of observables of the system at a prescribed final time...

A Data-Driven Simulation of HIV Spread Among Young Men Who Have Sex With Men: Role of Age and Race Mixing and STIs.

Young men who have sex with men (YMSM) in the United States have a high HIV incidence with substantial racial disparities that are poorly understood. We use a data-driven simulation model to understand the impact of network-level mechanisms and sexually transmitted infections on the spread of HIV among YMSM. We designed and parameterized a stochastic agent-based network simulation model using results of a longitudinal cohort study of YMSM in Chicago. Within this model, YMSM formed and dissolved partnerships over time, and partnership types were stratified by length of partnership, sex, and age of the partner. In each partnership, HIV, gonorrhea, and chlamydia could be transmitted. Counterfactual scenarios were run to examine drivers of HIV. Over a 15-year simulation, the HIV epidemic among YMSM continued to rise, with Latino/white YMSM facing a steeper increase in the HIV burden compared with black YMSM. YMSM in partnerships with older MSM, in particular black YMSM with older black MSM, were at highest risk for HIV, and 1 infection prevented with an older partner would prevent 0.8 additional infections among YMSM. Additionally, racial disparities in HIV were driven by differences in the HIV prevalence of YMSM partners. Finally, of all HIV infections among YMSM, 14.6% were attributable to NG and CT infections. Network-level mechanisms and sexually transmitted infections play a significant role in the spread of HIV and in racial disparities among YMSM. HIV prevention efforts should target YMSM across race, and interventions focusing on YMSM partnerships with older MSM might be highly effective.

The Spatial Chemical Langevin Equation and Reaction Diffusion Master Equations: moments and qualitative solutions.

BackgroundIt has been established that stochastic effects play an important role in spatio-temporal biochemical networks. A popular method of representing such stochastic systems is the Reaction Diffusion Master Equation (RDME). However, simulating sample paths from the RDME can be computationally expensive, particularly at large populations. Here we investigate an uncommon, but much faster alternative: the Spatial Chemical Langevin Equation (SCLE).MethodsWe investigate moment equations and correlation functions analytically, then we compare sample paths and moments of the SCLE to the RDME and associated deterministic solutions. Sample paths are generated computationally by the Next Subvolume method (RDME) and the Euler-Maruyama method (SCLE), while a deterministic solution is obtained with an Euler method. We consider the Gray-Scott model, a well-known pattern generating system, and a predator–prey system with spatially inhomogeneous parameters as sample applications.ResultsFor linear reaction networks, it is well known that the first order moments of all three approaches match, that the RDME and SCLE match to the second moment, and that all approaches diverge at third order moments. For non-linear reaction networks, differential equations governing moments do not form a closed system, but a general moment equation can be compared term wise. All approaches match at the leading order, and the RDME and SCLE match at the second leading order. As expected, the SCLE captures many dynamics of the RDME where deterministic methods fail to represent them. However, areas of the parameter space in the Gray-Scott model exist where either the SCLE and RDME give qualitatively different predictions, or the RDME predicts patterns, while the SCLE does not.ConclusionsThe SCLE provides a fast alternative to existing methods for simulation of spatial stochastic biochemical networks, capturing many aspects of dynamics represented by the RDME. This becomes very useful in search of quantitative parameters yielding desired qualitative solutions. However, there exist parameter sets where both the qualitative and quantitative behaviour of the SCLE can differ when compared to the RDME, so care should be taken in its use for applications demanding greater accuracy.Electronic supplementary materialThe online version of this article (doi:10.1186/s12976-015-0001-6) contains supplementary material, which is available to authorized users.

Color and degree of interspecific synchrony of environmental noise affect the variability of complex ecological networks

The fundamental debate on complexity–stability relationships in ecosystems is becoming more important in the face of dramatic contemporary changes. Most research using network approaches to address this challenge has focused on predator–prey interactions and static networks. We describe a stochastic ecological network simulation model that combines predator–prey interactions with mutualism, parasitism and basal species competition. Network topology is based on a generalized niche model, while temporal dynamics are specified using bioenergetic models with noise terms. We use the model to explore the effects of non-predator–prey interactions, color of environmental noise, and the degree of synchronization of environmental noise across species on the coefficients of variation of total ecosystem energy content and Shannon entropy over time. In regression trees derived by binary recursive partitioning, the presence or absence of synchrony gave the greatest difference in the means of data points for both system energy and Shannon entropy, followed in turn by white versus colored noise and pink versus red and black noise. The effects are present despite the large variation in the Monte Carlo simulations reflecting the variability of real ecosystems. Non-predator–prey interactions explained relatively small proportions of the total deviance, and each had different effect signs depending on the presence of the other interaction types and on whether energy or entropy was measured. These results underscore the importance of modeling more realistic colors of environmental noise in understanding and predicting the dynamics of food webs and ecological communities.