scholarly journals The COM-Poisson Process for Stochastic Modeling of Osmotic Inactivation Dynamics of Listeria monocytogenes

2021 ◽  
Vol 12 ◽  
Author(s):  
Pierluigi Polese ◽  
Manuela Del Torre ◽  
Mara Lucia Stecchini
Keyword(s):  
Listeria Monocytogenes ◽  
Poisson Process ◽  
Poisson Distribution ◽  
Population Distribution ◽  
Salt Content ◽  
Total Variance ◽  
Good Concordance ◽  
The One ◽  
Osmotic Treatment ◽  
Over Dispersion

Controlling harmful microorganisms, such as Listeria monocytogenes, can require reliable inactivation steps, including those providing conditions (e.g., using high salt content) in which the pathogen could be progressively inactivated. Exposure to osmotic stress could result, however, in variation in the number of survivors, which needs to be carefully considered through appropriate dispersion measures for its impact on intervention practices. Variation in the experimental observations is due to uncertainty and biological variability in the microbial response. The Poisson distribution is suitable for modeling the variation of equi-dispersed count data when the naturally occurring randomness in bacterial numbers it is assumed. However, violation of equi-dispersion is quite often evident, leading to over-dispersion, i.e., non-randomness. This article proposes a statistical modeling approach for describing variation in osmotic inactivation of L. monocytogenes Scott A at different initial cell levels. The change of survivors over inactivation time was described as an exponential function in both the Poisson and in the Conway-Maxwell Poisson (COM-Poisson) processes, with the latter dealing with over-dispersion through a dispersion parameter. This parameter was modeled to describe the occurrence of non-randomness in the population distribution, even the one emerging with the osmotic treatment. The results revealed that the contribution of randomness to the total variance was dominant only on the lower-count survivors, while at higher counts the non-randomness contribution to the variance was shown to increase the total variance above the Poisson distribution. When the inactivation model was compared with random numbers generated in computer simulation, a good concordance between the experimental and the modeled data was obtained in the COM-Poisson process.

scholarly journals Modeling Stochastic Variability in the Numbers of Surviving Salmonella enterica, Enterohemorrhagic Escherichia coli, and Listeria monocytogenes Cells at the Single-Cell Level in a Desiccated Environment

2016 ◽  
Vol 83 (4) ◽  
Author(s):  
Kento Koyama ◽  
Hidekazu Hokunan ◽  
Mayumi Hasegawa ◽  
Shuso Kawamura ◽  
Shigenobu Koseki
Keyword(s):  
Escherichia Coli ◽  
Listeria Monocytogenes ◽  
Probability Distribution ◽  
Poisson Process ◽  
Poisson Distribution ◽  
Salmonella Enterica ◽  
Bacterial Cells ◽  
Content Type ◽  
Cell Numbers ◽  
Inactivation Process

ABSTRACT Despite effective inactivation procedures, small numbers of bacterial cells may still remain in food samples. The risk that bacteria will survive these procedures has not been estimated precisely because deterministic models cannot be used to describe the uncertain behavior of bacterial populations. We used the Poisson distribution as a representative probability distribution to estimate the variability in bacterial numbers during the inactivation process. Strains of four serotypes of Salmonella enterica, three serotypes of enterohemorrhagic Escherichia coli, and one serotype of Listeria monocytogenes were evaluated for survival. We prepared bacterial cell numbers following a Poisson distribution (indicated by the parameter λ, which was equal to 2) and plated the cells in 96-well microplates, which were stored in a desiccated environment at 10% to 20% relative humidity and at 5, 15, and 25°C. The survival or death of the bacterial cells in each well was confirmed by adding tryptic soy broth as an enrichment culture. Changes in the Poisson distribution parameter during the inactivation process, which represent the variability in the numbers of surviving bacteria, were described by nonlinear regression with an exponential function based on a Weibull distribution. We also examined random changes in the number of surviving bacteria using a random number generator and computer simulations to determine whether the number of surviving bacteria followed a Poisson distribution during the bacterial death process by use of the Poisson process. For small initial cell numbers, more than 80% of the simulated distributions (λ = 2 or 10) followed a Poisson distribution. The results demonstrate that variability in the number of surviving bacteria can be described as a Poisson distribution by use of the model developed by use of the Poisson process. IMPORTANCE We developed a model to enable the quantitative assessment of bacterial survivors of inactivation procedures because the presence of even one bacterium can cause foodborne disease. The results demonstrate that the variability in the numbers of surviving bacteria was described as a Poisson distribution by use of the model developed by use of the Poisson process. Description of the number of surviving bacteria as a probability distribution rather than as the point estimates used in a deterministic approach can provide a more realistic estimation of risk. The probability model should be useful for estimating the quantitative risk of bacterial survival during inactivation.

On inference in a one-dimensional mosaic and an M/G/∞ queue

1985 ◽  
Vol 17 (01) ◽  
pp. 210-229
Author(s):  
Peter Hall
Keyword(s):  
Poisson Process ◽  
Segment Length ◽  
One Dimensional ◽  
Estimation Procedures ◽  
The One

Suppose segments are distributed at random along a line, their locations being determined by a Poisson process. In the case where segment length is fixed, we compare efficiencies of several different estimates of Poisson intensity. The case of random segment length is also considered, and there we study estimation procedures based on empiric properties. The one-dimensional mosaic may be viewed as an M/G/∞ queue.

A Highway Traffic Model

1975 ◽  
Vol 12 (S1) ◽  
pp. 303-309
Author(s):  
Herbert Solomon
Keyword(s):  
Poisson Process ◽  
Poisson Distribution ◽  
Random Measure ◽  
Traffic Model ◽  
Highway Traffic ◽  
Intensity Parameter ◽  
Time Space ◽  
Random Line ◽  
Straight Line ◽  
Poisson Fields

The trajectory of a car traveling at a constant speed on an idealized infinite highway can be viewed as a straight line in the time-space plane. Entry times are governed by a Poisson process with intensity parameter A leading to all trajectories as random lines in a plane. The Poisson distribution of number of encounters of cars on the highway is developed through random line models and non-homogeneous Poisson fields, and its parameter, which depends on the specific random measure employed, is obtained explicitly.

scholarly journals A filtered renewal process as a model for a river flow

2005 ◽  
Vol 2005 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Poisson Process ◽  
Exponential Distribution ◽  
Renewal Process ◽  
River Flow ◽  
Realistic Model ◽  
Delaware River ◽  
The Usa ◽  
The One ◽  
Peak Value

Various models, based on a filtered Poisson process, are used for the flow of a river. The aim is to forecast the next peak value of the flow, given that another peak was observed not too long ago. The most realistic model is the one when the time between the successive peaks doesnothave an exponential distribution, as is often assumed. An application to the Delaware River, in the USA, is presented.

scholarly journals Bayesian probabilities for occurrence of large earthquakes in the seismogenic sources of Japan and Phillipine during the period 1998-2017

2001 ◽  
Vol 34 (4) ◽  
pp. 1619
Author(s):  
T. M. TSAPANOS ◽  
O. CH. GALANIS ◽  
S. D. MAVRIDOU ◽  
M. P. HELMl
Keyword(s):  
Seismic Hazard ◽  
Bayesian Statistics ◽  
Poisson Distribution ◽  
Bayesian Approach ◽  
Seismic Sources ◽  
Time Interval ◽  
Seismogenic Sources ◽  
The One ◽  
Large Earthquakes ◽  
The Bayesian Approach

The Bayesian statistics is adopted in 11 seismic sources of Japan and 14 of Philippine in order to estimate the probabilities of occurrence of large future earthquakes, assuming that earthquakes occurrence follows the Poisson distribution. The Bayesian approach applied represents the probability that a certain cut-off magnitude (or larger) will exceed in a given time interval of 20 years, that is 1998-2017. This cut-off magnitude is chosen the one with M=7.0 or greater. In this case we can consider these obtained probabilities as a seismic hazard presentation. More over curves are produced which present the fluctuation of the seismic hazard between these seismic sources. These graphs of varying probability are useful either for engineering or other practical purposes

scholarly journals Fractional negative binomial and Pólya processes

2018 ◽  
Vol 38 (1) ◽  
pp. 77-101
Author(s):  
Palaniappan Vellai Samy ◽  
Aditya Maheshwari
Keyword(s):  
Poisson Process ◽  
Negative Binomial ◽  
Random Variable ◽  
Infinitely Divisible ◽  
One Dimensional ◽  
Fractional Poisson Process ◽  
Negative Binomial Process ◽  
The One ◽  
Definition Of ◽  
Binomial Process

In this paper, we define a fractional negative binomial process FNBP by replacing the Poisson process by a fractional Poisson process FPP in the gamma subordinated form of the negative binomial process. It is shown that the one-dimensional distributions of the FPP and the FNBP are not infinitely divisible. Also, the space fractional Pólya process SFPP is defined by replacing the rate parameter λ by a gamma random variable in the definition of the space fractional Poisson process. The properties of the FNBP and the SFPP and the connections to PDEs governing the density of the FNBP and the SFPP are also investigated.

scholarly journals On the equivalence of various definitions of mixed poisson processes

2019 ◽  
Vol 69 (2) ◽  
pp. 453-468
Author(s):  
Demetrios P. Lyberopoulos ◽  
Nikolaos D. Macheras ◽  
Spyridon M. Tzaninis
Keyword(s):  
Probability Distribution ◽  
Poisson Process ◽  
Random Variable ◽  
Poisson Processes ◽  
Counting Processes ◽  
Mixing Parameter ◽  
Mixed Poisson Process ◽  
Probability Spaces ◽  
The One

Abstract Under mild assumptions the equivalence of the mixed Poisson process with mixing parameter a real-valued random variable to the one with mixing probability distribution as well as to the mixed Poisson process in the sense of Huang is obtained, and a characterization of each one of the above mixed Poisson processes in terms of disintegrations is provided. Moreover, some examples of “canonical” probability spaces admitting counting processes satisfying the equivalence of all above statements are given. Finally, it is shown that our assumptions for the characterization of mixed Poisson processes in terms of disintegrations cannot be omitted.

First displacement time of a tagged particle in a stochastic cluster in a simple exclusion process with random slow bonds

2019 ◽  
Vol 51 (03) ◽  
pp. 717-744
Author(s):  
Adriana Uquillas ◽  
Adilson Simonis
Keyword(s):  
Poisson Process ◽  
Exclusion Process ◽  
Upper And Lower Bounds ◽  
Density Profiles ◽  
Tagged Particle ◽  
Simple Exclusion Process ◽  
Discrete Torus ◽  
Simple Exclusion ◽  
The One ◽  
Initial Measure

AbstractWe consider the nearest-neighbour simple exclusion process on the one-dimensional discrete torus $\mathbb{T}_N=\mathbb{Z}/N\mathbb{Z}$ , with random rates $c_N=\{c_{x,N}\colon x \in \mathbb{T}_N\}$ defined in terms of a homogeneous Poisson process on $\mathbb{R}$ with intensity $\lambda$ . Given a realization of the Poisson process, the jump rate along the edge $\{x,x+1\}$ is 1 if there is not any Poisson mark in $ (x,x+1) $ ; otherwise, it is $\lambda/N,\, \lambda \in( 0,1]$ . The density profile of this process with initial measure associated to an initial profile $\rho_0\colon \mathbb{R} \rightarrow [0,1]$ , evolves as the solution of a bounded diffusion random equation. This result follows from an appropriate quenched hydrodynamic limit. If $\lambda=1$ then $\rho$ is discontinuous at each Poisson mark with passage through the slow bonds, otherwise the conductance at the slow bonds decreases meaning no passage through the slow bonds in the continuum. The main results are concerned with upper and lower quenched and annealed bounds of $T_j$ , where $T_j$ is the first displacement time of a tagged particle in a stochastic cluster of size j (the cluster is defined via specific macroscopic density profiles). It is possible to observe that when time t grows, then $\mathbb{P}\{T_j \geq t\}$ decays quadratically in both the upper and lower bounds, and falls as slow as the presence of more Poisson marks neighbouring the tagged particle, as expected.

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