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Journal articles on the topic 'Stochastic spread'

Author: Grafiati

Published: 3 June 2025

Last updated: 19 July 2025

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O'DONOGHUE, BRENDAN, MATTHEW PEACOCK, JACKY LEE, and LUCA CAPRIOTTI. "A SPREAD-RETURN MEAN-REVERTING MODEL FOR CREDIT SPREAD DYNAMICS." International Journal of Theoretical and Applied Finance 17, no. 03 (2014): 1450017. http://dx.doi.org/10.1142/s0219024914500174.

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In this paper, we propose a novel, analytically tractable, one-factor stochastic model for the dynamics of credit default swap (CDS) spreads and their returns, which we refer to as the spread-return mean-reverting (SRMR) model. The SRMR model can be seen as a hybrid of the Black–Karasinski model on spreads and the Ornstein–Uhlenbeck model on spread returns, and is able to capture empirically observed properties of CDS spreads and returns, including spread mean-reversion, heavy tails of the return distribution, and return autocorrelations. Although developed for modeling CDS spreads, the SRMR model has applications for many other stochastic processes with similar empirical properties, including more general rate processes.

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Jansen, Vincent A. A., Michael Turelli, and H. Charles J. Godfray. "Stochastic spread of Wolbachia." Proceedings of the Royal Society B: Biological Sciences 275, no. 1652 (2008): 2769–76. http://dx.doi.org/10.1098/rspb.2008.0914.

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Wolbachia are very common, maternally transmitted endosymbionts of insects. They often spread by a mechanism termed cytoplasmic incompatibility (CI) that involves reduced egg hatch when Wolbachia -free ova are fertilized by sperm from Wolbachia -infected males. Because the progeny of Wolbachia -infected females generally do not suffer CI-induced mortality, infected females are often at a reproductive advantage in polymorphic populations. Deterministic models show that Wolbachia that impose no costs on their hosts and have perfect maternal transmission will spread from arbitrarily low frequencies (though initially very slowly); otherwise, there will be a threshold frequency below which Wolbachia frequencies decline to extinction and above which they increase to fixation or a high stable equilibrium. Stochastic theory was used to calculate the probability of fixation in populations of different size for arbitrary current frequencies of Wolbachia , with special attention paid to the case of spread after the arrival of a single infected female. Exact results are given based on a Moran process that assumes a specific demographic model, and approximate results are obtained using the more general Wright–Fisher theory. A new analytical approximation for the probability of fixation is derived, which performs well for small population sizes. The significance of stochastic effects in the natural spread of Wolbachia and their relevance to the use of Wolbachia as a drive mechanism in vector and pest management are discussed.

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Braun, Willard J. "Assessing a Stochastic Fire Spread Simulator." Journal of Environmental Informatics 22, no. 1 (2013): 1–12. http://dx.doi.org/10.3808/jei.201300241.

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Morishita, Yasaburo. "A stochastic model of fire spread." Fire Science and Technology 5, no. 1 (1985): 1–10. http://dx.doi.org/10.3210/fst.5.1.

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Hu, Linchao, Mugen Huang, Moxun Tang, Jianshe Yu, and Bo Zheng. "Wolbachia spread dynamics in stochastic environments." Theoretical Population Biology 106 (December 2015): 32–44. http://dx.doi.org/10.1016/j.tpb.2015.09.003.

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Tan, W. Y., and H. Hsu. "Some stochastic models of AIDS spread." Statistics in Medicine 8, no. 1 (1989): 121–36. http://dx.doi.org/10.1002/sim.4780080112.

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Levendis, Alexis, and Eben Maré. "Efficient Pricing of Spread Options with Stochastic Rates and Stochastic Volatility." Journal of Risk and Financial Management 15, no. 11 (2022): 504. http://dx.doi.org/10.3390/jrfm15110504.

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Spread options are notoriously difficult to price without the use of Monte Carlo simulation. Some strides have been made in recent years through the application of Fourier transform methods; however, to date, these methods have only been applied to specific underlying processes including two-factor geometric Brownian motion (gBm) and three-factor stochastic volatility models. In this paper, we derive the characteristic function for the two-asset Heston–Hull–White model with a full correlation matrix and apply the two-dimensional fast Fourier transform (FFT) method to price equity spread options. Our findings suggest that the FFT is up to 50 times faster than Monte Carlo and yields similar accuracy. Furthermore, stochastic interest rates can have a material impact on long-dated out-of-the-money spread options.

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Tiešis, Vytautas. "The infection spread model among grouped drug users." Lietuvos matematikos rinkinys, no. III (December 17, 1999): 453–57. http://dx.doi.org/10.15388/lmd.1999.35693.

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The stochastic model of an infection spread among intravenous drug users was built in the case when a group of drug users shares one filled syringe. The impact of various factors to the rate of spread was investigated by the stochastic simulation.

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Jin, Yunguo, and Shouming Zhong. "Pricing Spread Options with Stochastic Interest Rates." Mathematical Problems in Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/734265.

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Although spread options have been extensively studied in the literature, few papers deal with the problem of pricing spread options with stochastic interest rates. This study presents three novel spread option pricing models that permit the interest rates to be random. The paper not only presents a good approach to formulate spread option pricing models with stochastic interest rates but also offers a new test bed to understand the dynamics of option pricing with interest rates in a variety of asset pricing models. We discuss the merits of the models and techniques presented by us in some asset pricing models. Finally, we use regular grid method to the calculation of the formula when underlying stock returns are continuous and a mixture of both the regular grid method and a Monte Carlo method to the one when underlying stock returns are discontinuous, and sensitivity analyses are presented.

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Lewis, M. A. "Spread rate for a nonlinear stochastic invasion." Journal of Mathematical Biology 41, no. 5 (2000): 430–54. http://dx.doi.org/10.1007/s002850000022.

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DE, S. "Stochastic model of population growth and spread." Bulletin of Mathematical Biology 49, no. 1 (1987): 1–11. http://dx.doi.org/10.1016/s0092-8240(87)80032-0.

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JEZEK, Z., B. GRAB, and H. DIXON. "STOCHASTIC MODEL FOR INTERHUMAN SPREAD OF MONREYPOX." American Journal of Epidemiology 126, no. 6 (1987): 1082–92. http://dx.doi.org/10.1093/oxfordjournals.aje.a114747.

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De, S. S. "Stochastic model of population growth and spread." Bulletin of Mathematical Biology 49, no. 1 (1987): 1–11. http://dx.doi.org/10.1007/bf02459957.

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Shabunin, A. V. "Stochastic SIRS+V model of infections spread." Izvestiya of Saratov University. Physics 25, no. 1 (2025): 67–75. https://doi.org/10.18500/1817-3020-2025-25-1-67-75.

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GANI, J., and R. J. SWIFT. "DETERMINISTIC AND STOCHASTIC MODELS FOR THE SPREAD OF CHOLERA." ANZIAM Journal 51, no. 2 (2009): 234–40. http://dx.doi.org/10.1017/s1446181110000027.

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AbstractIn this note, we study deterministic and stochastic models for the spread of cholera. The deterministic model for the total number of cholera cases fits the observed total number of cholera cases in some recent outbreaks. The stochastic model for the total number of cholera cases leads to a binomial type distribution with a mean that agrees with the deterministic model.

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Liang, Qiantong, Johnny Yang, Wai-Tong Louis Fan, and Wing-Cheong Lo. "Patch formation driven by stochastic effects of interaction between viruses and defective interfering particles." PLOS Computational Biology 19, no. 10 (2023): e1011513. http://dx.doi.org/10.1371/journal.pcbi.1011513.

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Defective interfering particles (DIPs) are virus-like particles that occur naturally during virus infections. These particles are defective, lacking essential genetic materials for replication, but they can interact with the wild-type virus and potentially be used as therapeutic agents. However, the effect of DIPs on infection spread is still unclear due to complicated stochastic effects and nonlinear spatial dynamics. In this work, we develop a model with a new hybrid method to study the spatial-temporal dynamics of viruses and DIPs co-infections within hosts. We present two different scenarios of virus production and compare the results from deterministic and stochastic models to demonstrate how the stochastic effect is involved in the spatial dynamics of virus transmission. We compare the spread features of the virus in simulations and experiments, including the formation and the speed of virus spread and the emergence of stochastic patchy patterns of virus distribution. Our simulations simultaneously capture observed spatial spread features in the experimental data, including the spread rate of the virus and its patchiness. The results demonstrate that DIPs can slow down the growth of virus particles and make the spread of the virus more patchy.

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Graw, Frederik, Danyelle N. Martin, Alan S. Perelson, Susan L. Uprichard, and Harel Dahari. "Quantification of Hepatitis C Virus Cell-to-Cell Spread Using a Stochastic Modeling Approach." Journal of Virology 89, no. 13 (2015): 6551–61. http://dx.doi.org/10.1128/jvi.00016-15.

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ABSTRACTIt has been proposed that viral cell-to-cell transmission plays a role in establishing and maintaining chronic infections. Thus, understanding the mechanisms and kinetics of cell-to-cell spread is fundamental to elucidating the dynamics of infection and may provide insight into factors that determine chronicity. Because hepatitis C virus (HCV) spreads from cell to cell and has a chronicity rate of up to 80% in exposed individuals, we examined the dynamics of HCV cell-to-cell spreadin vitroand quantified the effect of inhibiting individual host factors. Using a multidisciplinary approach, we performed HCV spread assays and assessed the appropriateness of different stochastic models for describing HCV focus expansion. To evaluate the effect of blocking specific host cell factors on HCV cell-to-cell transmission, assays were performed in the presence of blocking antibodies and/or small-molecule inhibitors targeting different cellular HCV entry factors. In all experiments, HCV-positive cells were identified by immunohistochemical staining and the number of HCV-positive cells per focus was assessed to determine focus size. We found that HCV focus expansion can best be explained by mathematical models assuming focus size-dependent growth. Consistent with previous reports suggesting that some factors impact HCV cell-to-cell spread to different extents, modeling results estimate a hierarchy of efficacies for blocking HCV cell-to-cell spread when targeting different host factors (e.g., CLDN1 > NPC1L1 > TfR1). This approach can be adapted to describe focus expansion dynamics under a variety of experimental conditions as a means to quantify cell-to-cell transmission and assess the impact of cellular factors, viral factors, and antivirals.IMPORTANCEThe ability of viruses to efficiently spread by direct cell-to-cell transmission is thought to play an important role in the establishment and maintenance of viral persistence. As such, elucidating the dynamics of cell-to-cell spread and quantifying the effect of blocking the factors involved has important implications for the design of potent antiviral strategies and controlling viral escape. Mathematical modeling has been widely used to understand HCV infection dynamics and treatment response; however, these models typically assume only cell-free virus infection mechanisms. Here, we used stochastic models describing focus expansion as a means to understand and quantify the dynamics of HCV cell-to-cell spreadin vitroand determined the degree to which cell-to-cell spread is reduced when individual HCV entry factors are blocked. The results demonstrate the ability of this approach to recapitulate and quantify cell-to-cell transmission, as well as the impact of specific factors and potential antivirals.

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Iftikhar, Mehwish, Ayesha Sohail, and Nadeem Ahmad. "DETERMINISTIC AND STOCHASTIC ANALYSIS OF DENGUE SPREAD MODEL." Biomedical Engineering: Applications, Basis and Communications 31, no. 03 (2019): 1950008. http://dx.doi.org/10.4015/s101623721950008x.

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In this paper, a novel approach is adopted to model and predict the transmission of the viral disease dengue. We have studied the dynamics of the dengue spread from vector to human and human to vector for a homogeneous population. An authentic technique has been employed to obtain the equilibria and thus the basic reproduction number, which is defined as the average of secondary infections produced when a single infected individual is introduced into a host population where each individual is a susceptible. The nonlinear extended model is solved numerically. The stability analysis is discussed in detail in the light of the numerical results and important axioms. The epidemiological dynamics are discussed and a graphical analysis is presented for different values of the constraints.

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Wang, X. Joey, John R. J. Thompson, W. John Braun, and Douglas G. Woolford. "Fitting a stochastic fire spread model to data." Advances in Statistical Climatology, Meteorology and Oceanography 5, no. 1 (2019): 57–66. http://dx.doi.org/10.5194/ascmo-5-57-2019.

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Abstract. As the climate changes, it is important to understand the effects on the environment. Changes in wildland fire risk are an important example. A stochastic lattice-based wildland fire spread model was proposed by Boychuk et al. (2007), followed by a more realistic variant (Braun and Woolford, 2013). Fitting such a model to data from remotely sensed images could be used to provide accurate fire spread risk maps, but an intermediate step on the path to that goal is to verify the model on data collected under experimentally controlled conditions. This paper presents the analysis of data from small-scale experimental fires that were digitally video-recorded. Data extraction and processing methods and issues are discussed, along with an estimation methodology that uses differential equations for the moments of certain statistics that can be derived from a sequential set of photographs from a fire. The interaction between model variability and raster resolution is discussed and an argument for partial validation of the model is provided. Visual diagnostics show that the model is doing well at capturing the distribution of key statistics recorded during observed fires.

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Fewster, R. M. "A Spatiotemporal Stochastic Process Model for Species Spread." Biometrics 59, no. 3 (2003): 640–49. http://dx.doi.org/10.1111/1541-0420.00074.

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Whitman, John, and Ciriyam Jayaprakash. "Stochastic modeling of influenza spread dynamics with recurrences." PLOS ONE 15, no. 4 (2020): e0231521. http://dx.doi.org/10.1371/journal.pone.0231521.

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Jacquez, JohnA. "Spread of epidemics: stochastic modeling and data analysis." Mathematical Biosciences 102, no. 2 (1990): 229. http://dx.doi.org/10.1016/0025-5564(90)90064-6.

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Masoudian, Sahar, Jason Sharples, Zlatko Jovanoski, Isaac Towers, and Simon Watt. "Incorporating Stochastic Wind Vectors in Wildfire Spread Prediction." Atmosphere 14, no. 11 (2023): 1609. http://dx.doi.org/10.3390/atmos14111609.

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The stochastic nature of environmental factors that govern the behavior of fire, such as wind and fuel, exposes wildfire modeling to a degree of uncertainty. In order to produce more realistic wildfire predictions, it is, therefore, necessary to incorporate these uncertainties within wildfire models in a way that reflects the influence of environmental stochasticity on wildfire propagation. Otherwise, the risks of the potential danger of a given wildfire may be under-represented. Specifically, environmental stochasticity in the form of wind variability results in considerable uncertainty in the output of fire spread models. Here, we consider two stochastic wind models and their implementation in the spark fire simulator framework to capture the environmental uncertainty related to wind variability. The results are compared with the output from purely deterministic wildfire spread models and are discussed in the context of the potential ramifications for wildfire risk management.

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Bouttier, François, Benoît Vié, Olivier Nuissier, and Laure Raynaud. "Impact of Stochastic Physics in a Convection-Permitting Ensemble." Monthly Weather Review 140, no. 11 (2012): 3706–21. http://dx.doi.org/10.1175/mwr-d-12-00031.1.

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A stochastic physics scheme is tested in the Application of Research to Operations at Mesoscale (AROME) short-range convection-permitting ensemble prediction system. It is an adaptation of ECMWF’s stochastic perturbation of physics tendencies (SPPT) scheme. The probabilistic performance of the AROME model ensemble is found to be significantly improved, when verified against observations over two 2-week periods. The main improvement lies in the ensemble reliability and the spread–skill consistency. Probabilistic scores for several weather parameters are improved. The tendency perturbations have zero mean, but the stochastic perturbations have systematic effects on the model output, which explains much of the score improvement. Ensemble spread is an increasing function of the SPPT space and time correlations. A case study reveals that stochastic physics do not simply increase ensemble spread, they also tend to smooth out high-spread areas over wider geographical areas. Although the ensemble design lacks surface perturbations, there is a significant end impact of SPPT on low-level fields through physical interactions in the atmospheric model.

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Andrejczuk, M., F. C. Cooper, S. Juricke, T. N. Palmer, A. Weisheimer, and L. Zanna. "Oceanic Stochastic Parameterizations in a Seasonal Forecast System." Monthly Weather Review 144, no. 5 (2016): 1867–75. http://dx.doi.org/10.1175/mwr-d-15-0245.1.

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Stochastic parameterization provides a methodology for representing model uncertainty in ensemble forecasts. Here the impact on forecast reliability over seasonal time scales of three existing stochastic parameterizations in the ocean component of a coupled model is studied. The relative impacts of these schemes upon the ocean mean state and ensemble spread are analyzed. The oceanic variability induced by the atmospheric forcing of the coupled system is, in most regions, the major source of ensemble spread. The largest impact on spread and bias came from the stochastically perturbed parameterization tendency (SPPT) scheme, which has proven particularly effective in the atmosphere. The key regions affected are eddy-active regions, namely, the western boundary currents and the Southern Ocean where ensemble spread is increased. However, unlike its impact in the atmosphere, SPPT in the ocean did not result in a significant decrease in forecast error on seasonal time scales. While there are good grounds for implementing stochastic schemes in ocean models, the results suggest that they will have to be more sophisticated. Some suggestions for next-generation stochastic schemes are made.

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Ünözkan, H., M. Yilmaz, and A. M. Dere. "A stochastic approach to number of corona virus cases." Journal of Applied Mathematics, Statistics and Informatics 16, no. 2 (2020): 67–83. http://dx.doi.org/10.2478/jamsi-2020-0010.

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Abstract This paper introduces a stochastic approach to case numbers of a pandemic disease. By defining the stochastic process random walk process is used. Some stochastic aspects for this disease are argued before stochastic study is started. During random walk process modeling new patients, recovering patients and dead conclusions are modelled and probabilities changes in some stages. Let the structure of this study includes vanishing process as a walk step, some wave happenings like big differences about spread speed as a big step in treatment- an effective vaccine or an influential chemical usage- a second corona virus pumping with virus mutation, a second global happening which bumping virus spread are defined as stages. This study only simulates a stochastic process of corona virus effects.

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Ogwuche, Otache Innocent, Ephraim Kator Iortyer, Alex Emonyi, and Michael Ali. "A STOCHASTIC DIFFERENTIAL EQUATION (SDE) BASED MODEL FOR THE SPREAD OF TUBERCULOSIS." FUDMA JOURNAL OF SCIENCES 7, no. 5 (2023): 9–17. http://dx.doi.org/10.33003/fjs-2023-0705-1990.

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Understanding dynamics of an infectious disease helps in designing appropriate strategies for containing its spread in a population. In this work, a deterministic and stochastic model of the transmission dynamics of Tuberculosis is developed and analyzed. The models involve the Susceptible, Exposed, Infectious and Recovered individuals. We computed the basic reproduction number and showed that for, the disease-free equilibrium is globally asymptotically stable. The resulting deterministic model was transformed into an equivalent stochastic model resulting in stochastic differential equation. The drift coefficient, the covariance matrix and the diffusion matrix were determined using the method proposed by Allen et al. (2008).

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Wolff, Ronald W. "Sample-path derivations of the excess, age, and spread distributions." Journal of Applied Probability 25, no. 2 (1988): 432–36. http://dx.doi.org/10.2307/3214453.

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The familiar limiting distributions of excess, age, and spread are derived on sample paths, where these distributions are fractions of time. Similar results are obtained for the distribution of remaining service at a queue. For stochastic processes, where specified limits exist as finite constants with probability 1, the derived sample-path results are shown to imply that the same limiting distributions hold, where in a stochastic setting, these distributions may be defined in a more conventional way.

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Wolff, Ronald W. "Sample-path derivations of the excess, age, and spread distributions." Journal of Applied Probability 25, no. 02 (1988): 432–36. http://dx.doi.org/10.1017/s0021900200041097.

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Kurtin, Danielle L., Daniel A. J. Parsons, and Scott M. Stagg. "VTES: a stochastic Python-based tool to simulate viral transmission." F1000Research 9 (October 5, 2020): 1198. http://dx.doi.org/10.12688/f1000research.26786.1.

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The spread of diseases like severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in human populations involve a large number of variables, making it difficult to predict how it will spread across communities and populations. Reduced representation simulations allow us to reduce the complexity of disease spread and model transmission based on a few key variables. Here we have created a Viral Transmission Education Simulator (VTES) that simulates the spread of disease through the interactions between circles representing individual people bouncing around a bounded, 2D plane. Infections are transmitted via person-to-person contact and the course of an outbreak can be tracked over time. Using this approach, we are able to simulate the influence of variables like infectivity, population density, and social distancing on the course of an outbreak. We also describe how VTES's code can be used to calculate R0 for the simulated pandemic. VTES is useful for modeling how small changes in variables that influence disease transmission can have large changes on the outcome of an epidemic. Additionally, VTES serves as an educational tool where users can easily visualize how disease spreads, and test how interventions, like masking, can influence an outbreak. VTES is designed to be simple and clear to encourage user modifications. These properties make VTES an educational tool that uses accessible, clear code and dynamic simulations to provide a richer understanding of the behaviors and factors underpinning a pandemic. VTES is available from: https://github.com/sstagg/disease-transmission.

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Grimit, Eric P., and Clifford F. Mass. "Measuring the Ensemble Spread–Error Relationship with a Probabilistic Approach: Stochastic Ensemble Results." Monthly Weather Review 135, no. 1 (2007): 203–21. http://dx.doi.org/10.1175/mwr3262.1.

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Abstract One widely accepted measure of the utility of ensemble prediction systems is the relationship between ensemble spread and deterministic forecast accuracy. Unfortunately, this relationship is often characterized by spread–error linear correlations, which oversimplify the true spread–error relationship and ignore the possibility that some end users have categorical sensitivities to forecast error. In the present paper, a simulation study is undertaken to estimate the idealized spread–error statistics for stochastic ensemble prediction systems of a finite size. Under a variety of spread–error metrics, the stochastic ensemble spread–error joint distributions are characterized by increasing scatter as the ensemble spread grows larger. A new method is introduced that recognizes the inherent nonlinearity of spread–error joint distributions and capitalizes on the fact that the probability of large forecast errors increases with ensemble spread. The ensemble spread–error relationship is measured by the skill of probability forecasts that are constructed from a history of ensemble-mean forecast errors using only cases with similar ensemble spread. Thus, the value of ensemble spread information is quantified by the ultimate benefit that is realized by end users of the probability forecasts based on these conditional-error climatologies. It is found that the skill of conditional-error-climatology forecasts based on stochastic ensemble spread is nearly equal to the skill of probability forecasts constructed directly from the raw ensemble statistics. The skill is largest for cases with anomalous spread and smallest for cases with near-normal spread. These results reinforce the findings of earlier studies and affirm that the temporal variability of ensemble spread controls its potential value as a predictor. Additionally, it is found that the skill of spread-based error probability forecasts is maximized when the chosen spread metric is consistent with the end user’s cost function.

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Mahboubi, Arash, Seyit Camtepe, and Keyvan Ansari. "Stochastic Modeling of IoT Botnet Spread: A Short Survey on Mobile Malware Spread Modeling." IEEE Access 8 (2020): 228818–30. http://dx.doi.org/10.1109/access.2020.3044277.

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Hong, Jyy-I. "Limiting Behaviors of Stochastic Spread Models Using Branching Processes." Axioms 12, no. 7 (2023): 652. http://dx.doi.org/10.3390/axioms12070652.

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In this paper, we introduce a spread model using multi-type branching processes to investigate the evolution of the population during a pandemic in which individuals are classified into different types. We study some limiting behaviors of the population including the growth rate of the population and the spread rate of each type. In particular, the work in this paper focuses on the cases where the offspring mean matrices are non-primitive but can be decomposed into two primitive components, A and B, with maximal eigenvalues ρA and ρB, respectively. It is shown that the growth rate and the spread rate heavily depend on the conditions of these two maximal eigenvalues and are related to the corresponding eigenvectors. In particular, we find the spread rates for the case with ρB>ρA>1 and the case with ρA>ρB>1. In addition, some numerical examples and simulations are also provided to support the theoretical results.

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Zhang, Liang, Xinghao Wang, and Xiaobing Zhang. "Dynamics of a Stochastic Vector-Borne Model with Plant Virus Disease Resistance and Nonlinear Incidence." Symmetry 16, no. 9 (2024): 1122. http://dx.doi.org/10.3390/sym16091122.

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Symmetry in mathematical models often refers to invariance under certain transformations. In stochastic models, symmetry considerations must also account for the probabilistic nature of inter- actions and events. In this paper, a stochastic vector-borne model with plant virus disease resistance and nonlinear incidence is investigated. By constructing suitable stochastic Lyapunov functions, we show that if the related threshold R0s<1, then the disease will be extinct. By using the reproduction number R0, we establish sufficient conditions for the existence of ergodic stationary distribution to the stochastic model. Furthermore, we explore the results graphically in numerical section and find that random fluctuations introduced in the stochastic model can suppress the spread of the disease, except for increasing plant virus disease resistance and decreasing the contact rate between infected plants and susceptible vectors. The results reveal the correlation between symmetry and stochastic vector-borne models and can provide deeper insights into the dynamics of disease spread and control, potentially leading to more effective and efficient management strategies.

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Teixeira, João, and Carolyn A. Reynolds. "Stochastic Nature of Physical Parameterizations in Ensemble Prediction: A Stochastic Convection Approach." Monthly Weather Review 136, no. 2 (2008): 483–96. http://dx.doi.org/10.1175/2007mwr1870.1.

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Abstract In this paper it is argued that ensemble prediction systems can be devised in such a way that physical parameterizations of subgrid-scale motions are utilized in a stochastic manner, rather than in a deterministic way as is typically done. This can be achieved within the context of current physical parameterization schemes in weather and climate prediction models. Parameterizations are typically used to predict the evolution of grid-mean quantities because of unresolved subgrid-scale processes. However, parameterizations can also provide estimates of higher moments that could be used to constrain the random determination of the future state of a certain variable. The general equations used to estimate the variance of a generic variable are briefly discussed, and a simplified algorithm for a stochastic moist convection parameterization is proposed as a preliminary attempt. Results from the implementation of this stochastic convection scheme in the Navy Operational Global Atmospheric Prediction System (NOGAPS) ensemble are presented. It is shown that this method is able to generate substantial tropical perturbations that grow and “migrate” to the midlatitudes as forecast time progresses while moving from the small scales where the perturbations are forced to the larger synoptic scales. This stochastic convection method is able to produce substantial ensemble spread in the Tropics when compared with results from ensembles created from initial-condition perturbations. Although smaller, there is still a sizeable impact of the stochastic convection method in terms of ensemble spread in the extratropics. Preliminary simulations with initial-condition and stochastic convection perturbations together in the same ensemble system show a promising increase in ensemble spread and a decrease in the number of outliers in the Tropics.

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Jankov, Isidora, Judith Berner, Jeffrey Beck, et al. "A Performance Comparison between Multiphysics and Stochastic Approaches within a North American RAP Ensemble." Monthly Weather Review 145, no. 4 (2017): 1161–79. http://dx.doi.org/10.1175/mwr-d-16-0160.1.

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Abstract A stochastic parameter perturbation (SPP) scheme consisting of spatially and temporally varying perturbations of uncertain parameters in the Grell–Freitas convective scheme and the Mellor–Yamada–Nakanishi–Niino planetary boundary scheme was developed within the Rapid Refresh ensemble system based on the Weather Research and Forecasting Model. Alone the stochastic parameter perturbations generate insufficient spread to be an alternative to the operational configuration that utilizes combinations of multiple parameterization schemes. However, when combined with other stochastic parameterization schemes, such as the stochastic kinetic energy backscatter (SKEB) scheme or the stochastic perturbation of physics tendencies (SPPT) scheme, the stochastic ensemble system has comparable forecast performance. An additional analysis quantifies the added value of combining SPP and SPPT over an ensemble that uses SPPT only, which is generally beneficial, especially for surface variables. The ensemble combining all three stochastic methods consistently produces the best spread–skill ratio and generally outperforms the multiphysics ensemble. The results of this study indicate that using a single-physics suite ensemble together with stochastic methods is an attractive alternative to multiphysics ensembles and should be considered in the design of future high-resolution regional and global ensembles.

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Horii, Maya, Aidan Gould, Zachary Yun, Jaideep Ray, Cosmin Safta, and Tarek Zohdi. "Calibration verification for stochastic agent-based disease spread models." PLOS ONE 19, no. 12 (2024): e0315429. https://doi.org/10.1371/journal.pone.0315429.

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Accurate disease spread modeling is crucial for identifying the severity of outbreaks and planning effective mitigation efforts. To be reliable when applied to new outbreaks, model calibration techniques must be robust. However, current methods frequently forgo calibration verification (a stand-alone process evaluating the calibration procedure) and instead use overall model validation (a process comparing calibrated model results to data) to check calibration processes, which may conceal errors in calibration. In this work, we develop a stochastic agent-based disease spread model to act as a testing environment as we test two calibration methods using simulation-based calibration, which is a synthetic data calibration verification method. The first calibration method is a Bayesian inference approach using an empirically-constructed likelihood and Markov chain Monte Carlo (MCMC) sampling, while the second method is a likelihood-free approach using approximate Bayesian computation (ABC). Simulation-based calibration suggests that there are challenges with the empirical likelihood calculation used in the first calibration method in this context. These issues are alleviated in the ABC approach. Despite these challenges, we note that the first calibration method performs well in a synthetic data model validation test similar to those common in disease spread modeling literature. We conclude that stand-alone calibration verification using synthetic data may benefit epidemiological researchers in identifying model calibration challenges that may be difficult to identify with other commonly used model validation techniques.

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Almeida, Rodolfo Maduro, and Elbert E. N. Macau. "Stochastic cellular automata model for wildland fire spread dynamics." Journal of Physics: Conference Series 285 (March 1, 2011): 012038. http://dx.doi.org/10.1088/1742-6596/285/1/012038.

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Gibson, G. J. "Investigating Mechanisms of Spatiotemporal Epidemic Spread Using Stochastic Models." Phytopathology® 87, no. 2 (1997): 139–46. http://dx.doi.org/10.1094/phyto.1997.87.2.139.

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Kim, Yoora, Kyunghan Lee, and Ness B. Shroff. "On Stochastic Confidence of Information Spread in Opportunistic Networks." IEEE Transactions on Mobile Computing 15, no. 4 (2016): 909–23. http://dx.doi.org/10.1109/tmc.2015.2431711.

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DRABO, Abdoul Karim, Frédéric BERE, Sibiri Narcisse DOLEMWEOGO, and S. P. Clovis NITIEMA. "A STOCHASTIC MODEL FOR THE SPREAD OF HUMAN PLASMODIA." Advances in Differential Equations and Control Processes 30, no. 4 (2023): 363–83. http://dx.doi.org/10.17654/0974324323020.

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Liu, Fang, and Yi Zheng. "Modeling Spread of Information in Finite Hierarchical Networks." Advanced Materials Research 791-793 (September 2013): 1778–81. http://dx.doi.org/10.4028/www.scientific.net/amr.791-793.1778.

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A stochastic model of spreading information in an online community networks with finite populations is introduced. The impact of finite population size and cumulative effect on networks with two levels mixing is assessed. A number of explicit results are derived by using the computational methods of Markov chain path integral.

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Buehner, Mark. "Local Ensemble Transform Kalman Filter with Cross Validation." Monthly Weather Review 148, no. 6 (2020): 2265–82. http://dx.doi.org/10.1175/mwr-d-19-0402.1.

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Abstract Many ensemble data assimilation (DA) approaches suffer from the so-called inbreeding problem. As a consequence, there is an excessive reduction in ensemble spread by the DA procedure, causing the analysis ensemble spread to systematically underestimate the uncertainty of the ensemble mean analysis. The stochastic EnKF used for operational NWP in Canada largely avoids this problem by applying cross validation, that is, using an independent subset of ensemble members for updating each member. The goal of the present study is to evaluate two new variations of the local ensemble transform Kalman filter (LETKF) that also incorporate cross validation. In idealized numerical experiments with Gaussian-distributed background ensembles, the two new LETKF approaches are shown to produce reliable analysis ensembles such that the ensemble spread closely matches the uncertainty of the ensemble mean, without any ensemble inflation. In ensemble DA experiments with highly nonlinear idealized forecast models, the deterministic version of the LETKF with cross validation quickly diverges, but the stochastic version produces better results, nearly identical to the stochastic EnKF with cross validation. In the context of a regional NWP system, ensemble DA experiments are performed with the two new LETKF-based approaches with cross validation, the standard LETKF, and the stochastic EnKF. All approaches with cross validation produce similar ensemble spread at the first analysis time, though the amplitude of the changes to the individual members is larger with the stochastic approaches. Over the 10-day period of the experiments, the fit of the ensemble mean background state to radiosonde observations is statistically indistinguishable for all approaches evaluated.

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LI, HAIJIAO, and KUAN YANG. "ASYMPTOTIC BEHAVIOUR OF THE STOCHASTIC MAKI–THOMPSON MODEL WITH A FORGETTING MECHANISM ON OPEN POPULATIONS." ANZIAM Journal 62, no. 2 (2020): 185–208. http://dx.doi.org/10.1017/s1446181120000176.

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AbstractRumours have become part of our daily lives, and their spread has a negative impact on a variety of human affairs. Therefore, how to control the spread of rumours is an important topic. In this paper, we extend the classic Maki–Thompson model from a deterministic framework to a stochastic framework with a forgetting mechanism, because real-world person-to-person communications are inevitably affected by random factors. By constructing suitable stochastic Lyapunov functions, we show that the asymptotic behaviour of the stochastic rumour model is governed by the basic reproductive number. If this number is less than one, then the solution of the stochastic rumour model oscillates around the rumour-free equilibrium under extra mild conditions, indicating the extinction of the rumour with a probability of one. Otherwise, the solution always fluctuates around the endemic equilibrium under certain parametric restrictions, implying that the rumour will continually persist. In addition, we discuss a possible intervention strategy that stops the spread of rumours by strengthening the intensity of white noise, which is very different from the deterministic rumour model without white noise. Also, numerical simulations are conducted to support our analytical results.

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AOKI, YOSHITSUGU. "STOCHASTIC ONE-DIMENSIONAL DISCRETE SPACE MODEL FOR URBAN FIRE SPREAD : A theoretical analyses on stochastic spread of fire in urban area ; Part 1." Journal of Architecture, Planning and Environmental Engineering (Transactions of AIJ) 381 (1987): 111–21. http://dx.doi.org/10.3130/aijax.381.0_111.

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Ekanayake, Amy J. "Stochastic SIS metapopulation models for the spread of disease among species in a fragmented landscape." International Journal of Biomathematics 09, no. 04 (2016): 1650055. http://dx.doi.org/10.1142/s1793524516500558.

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Two stochastic models are derived for a susceptible–infectious–susceptible epidemic spreading through a metapopulation: a continuous time Markov chain (CTMC) model and an Itô stochastic differential equation (SDE) model. The stochastic models are numerically compared. Close agreement suggests that computationally intense CTMC simulations can be approximated by simpler SDE simulations. Differential equations for the moments of the SDE probability distribution are also derived, the steady states are solved numerically using a moment closure technique, and these results are compared to simulations. The moment closure technique only coarsely approximates simulation results. The effect of model parameters on stability of the disease-free equilibrium is also numerically investigated.

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Datta, Samik, James C. Bull, Giles E. Budge, and Matt J. Keeling. "Modelling the spread of American foulbrood in honeybees." Journal of The Royal Society Interface 10, no. 88 (2013): 20130650. http://dx.doi.org/10.1098/rsif.2013.0650.

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We investigate the spread of American foulbrood (AFB), a disease caused by the bacterium Paenibacillus larvae , that affects bees and can be extremely damaging to beehives. Our dataset comes from an inspection period carried out during an AFB epidemic of honeybee colonies on the island of Jersey during the summer of 2010. The data include the number of hives of honeybees, location and owner of honeybee apiaries across the island. We use a spatial SIR model with an underlying owner network to simulate the epidemic and characterize the epidemic using a Markov chain Monte Carlo (MCMC) scheme to determine model parameters and infection times (including undetected ‘occult’ infections). Likely methods of infection spread can be inferred from the analysis, with both distance- and owner-based transmissions being found to contribute to the spread of AFB. The results of the MCMC are corroborated by simulating the epidemic using a stochastic SIR model, resulting in aggregate levels of infection that are comparable to the data. We use this stochastic SIR model to simulate the impact of different control strategies on controlling the epidemic. It is found that earlier inspections result in smaller epidemics and a higher likelihood of AFB extinction.

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El Ansari, Youness, Ali El Myr, and Lahcen Omari. "Deterministic and Stochastic Study for an Infected Computer Network Model Powered by a System of Antivirus Programs." Discrete Dynamics in Nature and Society 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/3540278.

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We investigate the various conditions that control the extinction and stability of a nonlinear mathematical spread model with stochastic perturbations. This model describes the spread of viruses into an infected computer network which is powered by a system of antivirus software. The system is analyzed by using the stability theory of stochastic differential equations and the computer simulations. First, we study the global stability of the virus-free equilibrium state and the virus-epidemic equilibrium state. Furthermore, we use the Itô formula and some other theoretical theorems of stochastic differential equation to discuss the extinction and the stationary distribution of our system. The analysis gives a sufficient condition for the infection to be extinct (i.e., the number of viruses tends exponentially to zero). The ergodicity of the solution and the stationary distribution can be obtained if the basic reproduction number Rp is bigger than 1, and the intensities of stochastic fluctuations are small enough. Numerical simulations are carried out to illustrate the theoretical results.

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Agung Pratama and Danu Ariandi. "Stochastic SEIR Model for Simulating Epidemic Dynamics in Limited Populations." Switch : Jurnal Sains dan Teknologi Informasi 3, no. 1 (2024): 114–25. https://doi.org/10.62951/switch.v3i1.333.

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The stochastic SEIR model offers an innovative approach to understanding the spread of infectious diseases, particularly tuberculosis, in limited populations. This study adopts a stochastic model to capture random variability in individual interactions, often overlooked in deterministic models. The population is divided into four main categories: Susceptible (S), Exposed (E), Infected (I), and Recovered (R), with transitions between categories determined by probabilities based on epidemiological parameters. Through simulations, the model demonstrates its capability to depict more realistic patterns of disease spread, including fluctuations in case numbers and epidemic duration. The findings indicate that stochastic variability plays a crucial role in understanding the dynamics of tuberculosis transmission, especially in small populations or when the number of individual contacts is limited. The stochastic SEIR model can serve as an effective tool for policymakers to evaluate various intervention strategies, such as vaccination, transmission control, and treatment, as well as to design public health policies that are data-driven and adaptive to epidemiological uncertainties.

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López-García, Martín, and Theodore Kypraios. "A unified stochastic modelling framework for the spread of nosocomial infections." Journal of The Royal Society Interface 15, no. 143 (2018): 20180060. http://dx.doi.org/10.1098/rsif.2018.0060.

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Over the last years, a number of stochastic models have been proposed for analysing the spread of nosocomial infections in hospital settings. These models often account for a number of factors governing the spread dynamics: spontaneous patient colonization, patient–staff contamination/colonization, environmental contamination, patient cohorting or healthcare workers (HCWs) hand-washing compliance levels. For each model, tailor-designed methods are implemented in order to analyse the dynamics of the nosocomial outbreak, usually by means of studying quantities of interest such as the reproduction number of each agent in the hospital ward, which is usually computed by means of stochastic simulations or deterministic approximations. In this work, we propose a highly versatile stochastic modelling framework that can account for all these factors simultaneously, and which allows one to exactly analyse the reproduction number of each agent at the hospital ward during a nosocomial outbreak. By means of five representative case studies, we show how this unified modelling framework comprehends, as particular cases, many of the existing models in the literature. We implement various numerical studies via which we (i) highlight the importance of maintaining high hand-hygiene compliance levels by HCWs, (ii) support infection control strategies including to improve environmental cleaning during an outbreak and (iii) show the potential of some HCWs to act as super-spreaders during nosocomial outbreaks.

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