A bivariate birth-death process which approximates to the spread of a disease involving a vector

1972 ◽  
Vol 9 (1) ◽  
pp. 65-75 ◽  
Author(s):  
D. A. Griffiths
Keyword(s):  
Simple Model ◽  
Probability Distribution ◽  
General Class ◽  
Large Population ◽  
Vector Model ◽  
Death Process ◽  
The Mean ◽  
Probability Of Extinction ◽  
Over Time ◽  
Birth Death

A simple model for a bivariate birth-death process is proposed. This model approximates to the host-vector epidemic situation. An investigation of the transient process is made and the mean behaviour over time is explicitly found. The probability of extinction and the behaviour of the process conditional upon extinction are examined and the probability distribution of the cumulative population size to extinction is found. Appropriate circumstances are suggested under which the model might possibly be applied to malaria. The host-vector model is classified within a general class of models which represent large population approximations to epidemics involving two types of infectives.

A bivariate birth-death process which approximates to the spread of a disease involving a vector

1972 ◽  
Vol 9 (01) ◽  
pp. 65-75 ◽  
Author(s):  
D. A. Griffiths
Keyword(s):  
Simple Model ◽  
Probability Distribution ◽  
General Class ◽  
Large Population ◽  
Vector Model ◽  
Death Process ◽  
The Mean ◽  
Probability Of Extinction ◽  
Over Time ◽  
Birth Death

A simple model for a bivariate birth-death process is proposed. This model approximates to the host-vector epidemic situation. An investigation of the transient process is made and the mean behaviour over time is explicitly found. The probability of extinction and the behaviour of the process conditional upon extinction are examined and the probability distribution of the cumulative population size to extinction is found. Appropriate circumstances are suggested under which the model might possibly be applied to malaria. The host-vector model is classified within a general class of models which represent large population approximations to epidemics involving two types of infectives.

scholarly journals Stochastic models for interference between searching insect parasites

1989 ◽  
Vol 30 (3) ◽  
pp. 268-277 ◽  
Author(s):  
Phil Diamond
Keyword(s):  
Stationary Distribution ◽  
Intraspecific Competition ◽  
Death Process ◽  
Confluent Hypergeometric Functions ◽  
Large Populations ◽  
The Mean ◽  
The One ◽  
Globally Stable ◽  
Insect Parasites ◽  
Birth Death

AbstractCompetition between a finite number of searching insect parasites is modelled by differential equations and birth-death processes. In the one species case of intraspecific competition, the deterministic equilibrium is globally stable and, for large populations, approximates the mean of the stationary distribution of the process. For two species, both inter- and intraspecific competition occurs and the deterministic equilibrium is globally stable. When the birth-death process is reversible, it is shown that the mean of the stationary distribution is approximated by the equilibrium. Confluent hypergeometric functions of two variables are important to the theory.

On the parity of individuals in a branching process

1976 ◽  
Vol 13 (02) ◽  
pp. 219-230 ◽  
Author(s):  
J. Gani ◽  
I. W. Saunders
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Branching Process ◽  
Yeast Cells ◽  
Death Process ◽  
Second Moments ◽  
The Mean ◽  
Watson Process ◽  
Number Of Cells ◽  
Birth Death

This paper is concerned with the parity of a population of yeast cells, each of which may bud, not bud or die. Two multitype models are considered: a Galton-Watson process in discrete time, and its analogous birth-death process in continuous time. The mean number of cells with parity 0, 1, 2, … is obtained in both cases; some simple results are also derived for the second moments of the two processes.

On the parity of individuals in a branching process

1976 ◽  
Vol 13 (2) ◽  
pp. 219-230 ◽  
Author(s):  
J. Gani ◽  
I. W. Saunders
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Branching Process ◽  
Yeast Cells ◽  
Death Process ◽  
Second Moments ◽  
The Mean ◽  
Watson Process ◽  
Number Of Cells ◽  
Birth Death

This paper is concerned with the parity of a population of yeast cells, each of which may bud, not bud or die. Two multitype models are considered: a Galton-Watson process in discrete time, and its analogous birth-death process in continuous time. The mean number of cells with parity 0, 1, 2, … is obtained in both cases; some simple results are also derived for the second moments of the two processes.

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

Determination of the Probability Distribution of the Mean Sound Level

2010 ◽  
Vol 35 (4) ◽  
pp. 543-550 ◽  
Author(s):  
Wojciech Batko ◽  
Bartosz Przysucha
Keyword(s):  
Probability Distribution ◽  
Probability Distribution Function ◽  
Mean Value ◽  
Sound Level ◽  
Function Form ◽  
Noise Levels ◽  
Logarithmic Mean ◽  
The Mean ◽  
Estimation Of Uncertainty

AbstractAssessment of several noise indicators are determined by the logarithmic mean <img src="/fulltext-image.asp?format=htmlnonpaginated&src=P42524002G141TV8_html\05_paper.gif" alt=""/>, from the sum of independent random resultsL1;L2; : : : ;Lnof the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.

scholarly journals Planetary Nebulae in M31: Abundances, and comparison with bright Planetary Nebulae in the LMC

1997 ◽  
Vol 180 ◽  
pp. 475-476
Author(s):  
M. G. Richer ◽  
G. Stasińska ◽  
M. L. McCall
Keyword(s):  
Planetary Nebula ◽  
Luminosity Function ◽  
Large Population ◽  
Wavelength Region ◽  
Planetary Nebulae ◽  
Surprising Result ◽  
Population Synthesis ◽  
Abundance Distribution ◽  
Wide Range ◽  
The Mean

We have obtained spectra of 28 planetary nebulae in the bulge of M31 using the MOS spectrograph at the Canada-France-Hawaii Telescope. Typically, we observed the [O II] λ3727 to He I λ5876 wavelength region at a resolution of approximately 1.6 å/pixel. For 19 of the 21 planetary nebulae whose [OIII]λ5007 luminosities are within 1 mag of the peak of the planetary nebula luminosity function, our oxygen abundances are based upon a measured [OIII]λ4363 intensity, so they are based upon a measured electron temperature. The oxygen abundances cover a wide range, 7.85 dex < 12 + log(O/H) < 9.09 dex, but the mean abundance is surprisingly low, 12 + log(O/H)–8.64 ± 0.32 dex, i.e., roughly half the solar value (Anders & Grevesse 1989). The distribution of oxygen abundances is shown in Figure 1, where the ordinate indicates the number of planetary nebulae with abundances within ±0.1 dex of any point on the x-axis. The dashed line indicates the mean abundance, and the dotted lines indicate the ±1 σ points. The shape of this abundance distribution seems to indicate that the bulge of M31 does not contain a large population of bright, oxygen-rich planetary nebulae. This is a surprising result, for various population synthesis studies (e.g., Bica et al. 1990) have found a mean stellar metallicity approximately 0.2 dex above solar. This 0.5 dex discrepancy leads one to question whether the mean stellar metallicity is as high as the population synthesis results indicate or if such metal-rich stars produce bright planetary nebulae at all. This could be a clue concerning the mechanism responsible for the variation in the number of bright planetary nebulae observed per unit luminosity in different galaxies (e.g., Hui et al. 1993).

scholarly journals Kinetic analysis and optimisation of 18F-rhPSMA-7.3 PET imaging of prostate cancer

2021 ◽  
Author(s):  
Simona Malaspina ◽  
Vesa Oikonen ◽  
Anna Kuisma ◽  
Otto Ettala ◽  
Kalle Mattila ◽  
...  
Keyword(s):  
Prostate Cancer ◽  
Metastatic Disease ◽  
Uptake Kinetics ◽  
Whole Body ◽  
Target Area ◽  
Post Injection ◽  
The Mean ◽  
Pet Radiopharmaceutical ◽  
Time Frames ◽  
Over Time

Abstract Purpose This phase 1 open-label study evaluated the uptake kinetics of a novel theranostic PET radiopharmaceutical, 18F-rhPSMA-7.3, to optimise its use for imaging of prostate cancer. Methods Nine men, three with high-risk localised prostate cancer, three with treatment-naïve hormone-sensitive metastatic disease and three with castration-resistant metastatic disease, underwent dynamic 45-min PET scanning of a target area immediately post-injection of 300 MBq 18F-rhPSMA-7.3, followed by two whole-body PET/CT scans acquired from 60 and 90 min post-injection. Volumes of interest (VoIs) corresponding to prostate cancer lesions and reference tissues were recorded. Standardised uptake values (SUV) and lesion-to-reference ratios were calculated for 3 time frames: 35–45, 60–88 and 90–118 min. Net influx rates (Ki) were calculated using Patlak plots. Results Altogether, 44 lesions from the target area were identified. Optimal visual lesion detection started 60 min post-injection. The 18F-rhPSMA-7.3 signal from prostate cancer lesions increased over time, while reference tissue signals remained stable or decreased. The mean (SD) SUV (g/mL) at the 3 time frames were 8.4 (5.6), 10.1 (7) and 10.6 (7.5), respectively, for prostate lesions, 11.2 (4.3), 13 (4.8) and 14 (5.2) for lymph node metastases, and 4.6 (2.6), 5.7 (3.1) and 6.4 (3.5) for bone metastases. The mean (SD) lesion-to-reference ratio increases from the earliest to the 2 later time frames were 40% (10) and 59% (9), respectively, for the prostate, 65% (27) and 125% (47) for metastatic lymph nodes and 25% (19) and 32% (30) for bone lesions. Patlak plots from lesion VoIs signified almost irreversible uptake kinetics. Ki, SUV and lesion-to-reference ratio estimates showed good agreement. Conclusion 18F-rhPSMA-7.3 uptake in prostate cancer lesions was high. Lesion-to-background ratios increased over time, with optimal visual detection starting from 60 min post-injection. Thus, 18F-rhPSMA-7.3 emerges as a very promising PET radiopharmaceutical for diagnostic imaging of prostate cancer. Trial Registration NCT03995888 (24 June 2019).

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