Applications of branching processes to the final size of SIR epidemics

2010 ◽  
pp. 207-223 ◽  
Author(s):  
Frank Ball ◽  
Peter Neal
Keyword(s):  
Branching Processes ◽  
Final Size

Acquaintance Vaccination in an Epidemic on a Random Graph with Specified Degree Distribution

2013 ◽  
Vol 50 (04) ◽  
pp. 1147-1168 ◽  
Author(s):  
Frank Ball ◽  
David Sirl
Keyword(s):  
Random Graph ◽  
Degree Distribution ◽  
Numerical Study ◽  
Branching Processes ◽  
Large Population ◽  
Configuration Model ◽  
Vaccine Response ◽  
Final Size ◽  
Infinite Type ◽  
Type Spaces

We consider a stochastic SIR (susceptible → infective → removed) epidemic on a random graph with specified degree distribution, constructed using the configuration model, and investigate the ‘acquaintance vaccination’ method for targeting individuals of high degree for vaccination. Branching process approximations are developed which yield a post-vaccination threshold parameter, and the asymptotic (large population) probability and final size of a major outbreak. We find that introducing an imperfect vaccine response into the present model for acquaintance vaccination leads to sibling dependence in the approximating branching processes, which may then require infinite type spaces for their analysis and are generally not amenable to numerical calculation. Thus, we propose and analyse an alternative model for acquaintance vaccination, which avoids these difficulties. The theory is illustrated by a brief numerical study, which suggests that the two models for acquaintance vaccination yield quantitatively very similar disease properties.

scholarly journals Acquaintance Vaccination in an Epidemic on a Random Graph with Specified Degree Distribution

2013 ◽  
Vol 50 (4) ◽  
pp. 1147-1168 ◽  
Author(s):  
Frank Ball ◽  
David Sirl
Keyword(s):  
Random Graph ◽  
Degree Distribution ◽  
Numerical Study ◽  
Branching Processes ◽  
Large Population ◽  
Configuration Model ◽  
Vaccine Response ◽  
Final Size ◽  
Infinite Type ◽  
Type Spaces

We consider a stochastic SIR (susceptible → infective → removed) epidemic on a random graph with specified degree distribution, constructed using the configuration model, and investigate the ‘acquaintance vaccination’ method for targeting individuals of high degree for vaccination. Branching process approximations are developed which yield a post-vaccination threshold parameter, and the asymptotic (large population) probability and final size of a major outbreak. We find that introducing an imperfect vaccine response into the present model for acquaintance vaccination leads to sibling dependence in the approximating branching processes, which may then require infinite type spaces for their analysis and are generally not amenable to numerical calculation. Thus, we propose and analyse an alternative model for acquaintance vaccination, which avoids these difficulties. The theory is illustrated by a brief numerical study, which suggests that the two models for acquaintance vaccination yield quantitatively very similar disease properties.

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

Ultrastructure of myoepithelial cell in parotid gland

1988 ◽  
Vol 46 ◽  
pp. 342-343
Author(s):  
C. N. Sun
Keyword(s):  
Parotid Gland ◽  
Osmium Tetroxide ◽  
Individual Cell ◽  
Branching Processes ◽  
Muscle Cells ◽  
Myoepithelial Cells ◽  
Uranyl Acetate ◽  
Thin Sections ◽  
Gland Carcinoma ◽  
Parotid Gland Carcinoma

Myoepithelial cells have been observed in the prostate, harderian, apocrine, exocrine sweat and mammary glands. Such cells and their numerous branching processes form basket-like structures around the glandular acini. Their shapes are quite different from structures seen either in spindleshaped smooth muscle cells or skeletal muscle cells. These myoepithelial cells lie on the epithelial side of the basement membrane in the glands. This presentation describes the ultrastructure of such myoepithelial cells which have been found also in the parotid gland carcinoma from a 45-year old patient.Specimens were cut into small pieces about 1 mm3 and immediately fixed in 4 percent glutaraldehyde in phosphate buffer for two hours, then post-fixed in 1 percent buffered osmium tetroxide for 1 hour. After dehydration, tissues were embedded in Epon 812. Thin sections were stained with uranyl acetate and lead citrate. Ultrastructurally, the pattern of each individual cell showed wide variations.

Microstructural Development in Nb-Ti Multifilamentary Superconductors During Processing

1985 ◽  
Vol 43 ◽  
pp. 190-191
Author(s):  
A. W. West
Keyword(s):  
Heat Treatment ◽  
Critical Current Density ◽  
Copper Matrix ◽  
Wire Drawing ◽  
Heat Treatments ◽  
Microstructural Development ◽  
Final Size ◽  
Density Values ◽  
The Wire ◽  
Multifilamentary Superconductors

The influence of the filament microstructure on the critical current density values, Jc, of Nb-Ti multifilamentary superconducting composites has been well documented. However the development of these microstructures during composite processing is still under investigation.During manufacture, the multifilamentary composite is given several heat treatments interspersed in the wire-drawing schedule. Typically, these heat treatments are for 5 to 80 hours at temperatures between 523 and 573K. A short heat treatment of approximately 3 hours at 573K is usually given to the wire at final size. Originally this heat treatment was given to soften the copper matrix, but recent work has shown that it can markedly change both the Jc value and microstructure of the composite.

Regenerative Sampling and Monotonic Branching Processes.

1986 ◽  
Author(s):  
Stephen D. Durham ◽  
Kai F. Yu
Keyword(s):  
Branching Processes

THE MECHANISM OF FINAL SIZE CONTROL OF L10-FEPT NANOCRYSTALS

2016 ◽  
Vol 72 (9) ◽  
Author(s):  
Seyed Ali Sebt ◽  
Zahra Bamshad ◽  
Mohammad Reza Abolhassani
Keyword(s):  
Size Control ◽  
Final Size

On calculating extinction probabilities for branching processes in random environments

1969 ◽  
Vol 6 (03) ◽  
pp. 478-492 ◽  
Author(s):  
William E. Wilkinson
Keyword(s):  
Generating Functions ◽  
Infinite Sequence ◽  
Branching Processes ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Random Environments ◽  
Real Numbers ◽  
Discrete Time Markov Chain ◽  
Extinction Probabilities ◽  
Image Position

Consider a discrete time Markov chain {Zn } whose state space is the non-negative integers and whose transition probability matrix ║Pij ║ possesses the representation where {Pr }, r = 1,2,…, is a finite or denumerably infinite sequence of non-negative real numbers satisfying , and , is a corresponding sequence of probability generating functions. It is assumed that Z 0 = k, a finite positive integer.

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