The Final State of an Epidemic in a Large Heterogeneous Population with a Large Initial Number of Infectives

We describe some asymptotic properties of a general S–I–R epidemic process in a large heterogeneous population. We assume that the infectives behave independently, that each infective has a generally distributed random number of contacts with the others in the population, and that among the initial susceptibles there is an arbitrary initial distribution of susceptibility. For the case of a large number of initial infectives, we demonstrate the asymptotic normality of the final size distribution as well as convergence of the final distribution of susceptibility as the population size approaches infinity. The relationship between the mean of the limiting final size distribution and the initial heterogeneity of susceptibility is explored, for a parametric example.

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The Early and Final States of an Epidemic in a Large Heterogeneous Population by a Small Initial Number of Infectives

Advances in Applied Probability ◽

10.1017/s0001867800026483 ◽

1994 ◽

Vol 26 (03) ◽

pp. 671-689

Author(s):

Steven M. Butler

Keyword(s):

Random Number ◽

Death Process ◽

Time Interval ◽

Final States ◽

Birth And Death Process ◽

Initial Number ◽

Threshold Behavior ◽

Final State ◽

Epidemic Process ◽

Susceptibility To Infection

This paper describes the early and final properties of a general S–I–R epidemic process in which the infectives behave independently, each infective has a random number of contacts with the others in the population, and individuals vary in their susceptibility to infection. For the case of a large initial number of susceptibles and a small (finite) initial number of infectives, we derive the threshold behavior and the limiting distribution for the final state of the epidemic. Also, we show strong convergence of the epidemic process over any finite time interval to a birth and death process, extending the results of Ball (1983). These complement some results due to Butler (1994), who considers the case of a large initial number of infectives.

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Limit theorems and estimation theory for branching processes with an increasing random number of ancestors

Journal of Applied Probability ◽

10.2307/3215372 ◽

1997 ◽

Vol 34 (2) ◽

pp. 309-327 ◽

Cited By ~ 10

Author(s):

J. P. Dion ◽

N. M. Yanev

Keyword(s):

Limit Theorem ◽

Limit Theorems ◽

Random Number ◽

Branching Processes ◽

Asymptotic Properties ◽

Random Variables ◽

Transfer Theorem ◽

Asymptotically Normal ◽

The Mean ◽

Watson Process

This paper deals with a Bienaymé-Galton-Watson process having a random number of ancestors. Its asymptotic properties are studied when both the number of ancestors and the number of generations tend to infinity. This yields consistent and asymptotically normal estimators of the mean and the offspring distribution of the process. By exhibiting a connection with the BGW process with immigration, all results can be transported to the immigration case, under an appropriate sampling scheme. A key feature of independent interest is a new limit theorem for sums of a random number of random variables, which extends the Gnedenko and Fahim (1969) transfer theorem.

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Size distribution and meiotic competence of oocytes obtained from bitch ovaries at various stages of the oestrous cycle

Reproduction Fertility and Development ◽

10.1071/rd00098 ◽

2001 ◽

Vol 13 (3) ◽

pp. 151 ◽

Cited By ~ 31

Author(s):

Takeshige Otoi ◽

Aya Ooka ◽

Masako Murakami ◽

N.W. Kurniani Karja ◽

Tatsuyuki Suzuki

Keyword(s):

Size Distribution ◽

Relative Size ◽

Follicular Phase ◽

Oestrous Cycle ◽

The Other ◽

Three Stages ◽

The Mean ◽

The Relationship ◽

Meiotic Competence

The present study was conducted to examine the effects of the stage of the oestrous cycle on the meiotic competence of canine oocytes and also to investigate the relationship between the stage of the oestrous cycle and the relative size distribution of oocytes obtained from bitches at three stages of the cycle (anoestrus, follicular phase and dioestrus). Only healthy-looking cumulus–oocyte complexes were used for in vitro maturation and these were divided into three groups based on diameter (<110, 110 to <120 and ≥120 µm). The mean diameter of oocytes from ovaries at anoestrus, the follicular phase and dioestrus was 103.6, 119.2 and 107.7 µm, respectively. The percentage of large oocytes (120 µm) collected at the follicular phase was higher (P<0.01) than that collected at dioestrus and the percentage of oocytes ≥120 µm collected from ovaries at dioestrus was higher (P<0.01) than that collected at anoestrus. After culture for 72 h, significantly more oocytes reached metaphase II (MII) in the follicular phase than in the other stages (P<0.01), and more oocytes reached MII in dioestrus than in anoestrus (P<0.05). In the ≥120 µm group, the frequency of oocytes that resumed meiosis in the follicular phase was higher (P<0.05) than in the other stages. However, in the smaller diameter (<120 µm) groups, there were no significant differences between ovaries at different stages of the oestrous cycle with respect to the proportion of oocytes reaching each stage of meiosis. Thus, the oestrous cycle stage influences maturation frequency. Moreover, oocytes demonstrated a size-related ability to undergo meiotic maturation, irrespective of the stage of the oestrous cycle. These results suggest that the effects of the stage of the oestrous cycle may result from differences in the distribution of large oocytes.

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Limit theorems and estimation theory for branching processes with an increasing random number of ancestors

Journal of Applied Probability ◽

10.1017/s0021900200100968 ◽

1997 ◽

Vol 34 (02) ◽

pp. 309-327 ◽

Cited By ~ 2

Author(s):

J. P. Dion ◽

N. M. Yanev

Keyword(s):

Limit Theorem ◽

Limit Theorems ◽

Random Number ◽

Branching Processes ◽

Asymptotic Properties ◽

Random Variables ◽

Transfer Theorem ◽

Asymptotically Normal ◽

The Mean ◽

Watson Process

This paper deals with a Bienaymé-Galton-Watson process having a random number of ancestors. Its asymptotic properties are studied when both the number of ancestors and the number of generations tend to infinity. This yields consistent and asymptotically normal estimators of the mean and the offspring distribution of the process. By exhibiting a connection with the BGW process with immigration, all results can be transported to the immigration case, under an appropriate sampling scheme. A key feature of independent interest is a new limit theorem for sums of a random number of random variables, which extends the Gnedenko and Fahim (1969) transfer theorem.

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The Early and Final States of an Epidemic in a Large Heterogeneous Population by a Small Initial Number of Infectives

Advances in Applied Probability ◽

10.2307/1427814 ◽

1994 ◽

Vol 26 (3) ◽

pp. 671-689 ◽

Cited By ~ 2

Author(s):

Steven M. Butler

Keyword(s):

Random Number ◽

Death Process ◽

Time Interval ◽

Final States ◽

Birth And Death Process ◽

Initial Number ◽

Threshold Behavior ◽

Final State ◽

Epidemic Process ◽

Susceptibility To Infection

This paper describes the early and final properties of a general S–I–R epidemic process in which the infectives behave independently, each infective has a random number of contacts with the others in the population, and individuals vary in their susceptibility to infection. For the case of a large initial number of susceptibles and a small (finite) initial number of infectives, we derive the threshold behavior and the limiting distribution for the final state of the epidemic. Also, we show strong convergence of the epidemic process over any finite time interval to a birth and death process, extending the results of Ball (1983). These complement some results due to Butler (1994), who considers the case of a large initial number of infectives.

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Multi-Center Calibration of the Second Reference Material for Thromboplastin, Rabbit, Plain, Coded CRM 149R

Thrombosis and Haemostasis ◽

10.1055/s-0038-1648132 ◽

1991 ◽

Vol 65 (03) ◽

pp. 263-267 ◽

Cited By ~ 3

Author(s):

A M H P van den Besselaar ◽

R M Bertina

Keyword(s):

Reference Material ◽

Standard Error ◽

Standard Errors ◽

Sensitivity Index ◽

Long Term Stability ◽

Significant Bias ◽

The Mean ◽

The Relationship ◽

International Sensitivity Index

SummaryIn a collaborative trial of eleven laboratories which was performed mainly within the framework of the European Community Bureau of Reference (BCR), a second reference material for thromboplastin, rabbit, plain, was calibrated against its predecessor RBT/79. This second reference material (coded CRM 149R) has a mean International Sensitivity Index (ISI) of 1.343 with a standard error of the mean of 0.035. The standard error of the ISI was determined by combination of the standard errors of the ISI of RBT/79 and the slope of the calibration line in this trial.The BCR reference material for thromboplastin, human, plain (coded BCT/099) was also included in this trial for assessment of the long-term stability of the relationship with RBT/79. The results indicated that this relationship has not changed over a period of 8 years. The interlaboratory variation of the slope of the relationship between CRM 149R and RBT/79 was significantly lower than the variation of the slope of the relationship between BCT/099 and RBT/79. In addition to the manual technique, a semi-automatic coagulometer according to Schnitger & Gross was used to determine prothrombin times with CRM 149R. The mean ISI of CRM 149R was not affected by replacement of the manual technique by this particular coagulometer.Two lyophilized plasmas were included in this trial. The mean slope of relationship between RBT/79 and CRM 149R based on the two lyophilized plasmas was the same as the corresponding slope based on fresh plasmas. Tlowever, the mean slope of relationship between RBT/79 and BCT/099 based on the two lyophilized plasmas was 4.9% higher than the mean slope based on fresh plasmas. Thus, the use of these lyophilized plasmas induced a small but significant bias in the slope of relationship between these thromboplastins of different species.

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Evaluation of the Efficacy of ST2 and NT-proBNP in the Diagnosis and Prediction of Short- Term Prognosis in Heart Failure with Reduced Ejection Fraction

International Journal of Pharmaceutical and Clinical Research ◽

10.25258/ijpcr.v9i04.8539 ◽

2017 ◽

Vol 9 (04) ◽

Author(s):

Shivananda B Nayak ◽

Dharindra Sawh ◽

Brandon Scott ◽

Vestra Sears ◽

Kareshma Seebalack ◽

...

Keyword(s):

Heart Failure ◽

Ejection Fraction ◽

Cardiac Biomarkers ◽

Double Blind Study ◽

Short Term ◽

Double Blind ◽

Reduced Ejection Fraction ◽

The Mean ◽

Design And Methods ◽

The Relationship

Purpose: i) To determine the relationship between the cardiac biomarkers ST2 and NT-proBNP with ejection fraction (EF) in heart failure (HF) patients. ii) Assess whether a superiority existed between the aforementioned cardiac markers in diagnosing the HF with reduced EF. iii) Determine the efficacy of both biomarkers in predicting a 30-day cardiovascular event and rehospitalization in patients with HF with reduced EF iv) To assess the influence of age, gender, BMI, anaemia and renal failure on the ST2 and NT-proBNP levels. Design and Methods: A prospective double-blind study was conducted to obtain data from a sample of 64 cardiology patients. A blood sample was collected to test for ST2 and NT-proBNP. An echocardiogram (to obtain EF value), electrocardiogram and questionnaire were also obtained. Results: Of the 64 patients enrolled, 59.4% of the population had an EF less than 40%. At the end of the 30- day period, 7 patients were warded, 37 were not warded, one died and 17 were non respondent. Both biomarkers were efficacious at diagnosing HF with a reduced EF. However, neither of them were efficacious in predicting 30-day rehospitalization. The mean NT-proBNP values being: not rehospitalized (2114.7486) and 30 day rehospitalization (1008.42860) and the mean ST2 values being: not rehospitalized (336.1975), and 30-day rehospitalization. (281.9657). Conclusion: Neither ST2 or NT-proBNP was efficacious in predicting the short- term prognosis in HF with reduced EF. Both however were successful at confirming the diagnosis of HF in HF patients with reduced EF.

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Batch Precipitation of Lead Iodide

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19941301 ◽

1994 ◽

Vol 59 (6) ◽

pp. 1301-1304

Author(s):

Jaroslav Nývlt ◽

Stanislav Žáček

Keyword(s):

Aqueous Solution ◽

Particle Size ◽

Particle Size Distribution ◽

Size Distribution ◽

Crystal Size ◽

Lead Nitrate ◽

Lead Iodide ◽

Constant Rate ◽

Mean Size ◽

The Mean

Lead iodide was precipitated by a procedure in which an aqueous solution of potassium iodide at a concentration of 0.03, 0.10 or 0.20 mol l-1 was stirred while an aqueous solution of lead nitrate at one-half concentration was added at a constant rate. The mean size of the PbI2 crystals was determined by evaluating the particle size distribution, which was measured sedimentometrically. The dependence of the mean crystal size on the duration of the experiment exhibited a minimum for any of the concentrations applied. The reason for this is discussed.

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Correlation between fundus autofluorescence and visual function in patients with cone-rod dystrophy

Scientific Reports ◽

10.1038/s41598-021-81597-7 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Satoru Kanda ◽

Takumi Hara ◽

Ryosuke Fujino ◽

Keiko Azuma ◽

Hirotsugu Soga ◽

...

Keyword(s):

Visual Field ◽

Significant Relationship ◽

Fundus Autofluorescence ◽

Univariate Analysis ◽

Retrospective Chart Review ◽

Mean Deviation ◽

Wide Field ◽

The Mean ◽

The Relationship ◽

Field Imaging

AbstractThis study aimed to investigate the relationship between autofluorescence (AF) signal measured with ultra-wide field imaging and visual functions in patients with cone-rod dystrophy (CORD). A retrospective chart review was performed for CORD patients. We performed the visual field test and fundus autofluorescence (FAF) measurement and visualized retinal structures with optical coherence tomography (OCT) on the same day. Using binarised FAF images, we identified a low FAF area ratio (LFAR: low FAF/30°). Relationships between age and logMAR visual acuity (VA), central retinal thickness (CRT), central choroidal thickness (CCT), mean deviation (MD) value, and LFAR were investigated. Thirty-seven eyes of 21 CORD patients (8 men and 13 women) were enrolled. The mean patient age was 49.8 years. LogMAR VA and MD were 0.52 ± 0.47 and − 17.91 ± 10.59 dB, respectively. There was a significant relationship between logMAR VA and MD (p = 0.001). LogMAR VA significantly correlated with CRT (p = 0.006) but not with other parameters. Conversely, univariate analysis suggested a significant relationship between MD and LFAR (p = 0.001). In the multivariate analysis, LFAR was significantly associated with MD (p = 0.002). In conclusion, it is useful to measure the low FAF area in patients with CORD. The AF measurement reflects the visual field deterioration but not VA in CORD.

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