scholarly journals Who is the infector? General multi-type epidemics and real-time susceptibility processes

2019 ◽  
Vol 51 (2) ◽  
pp. 606-631
Author(s):  
Tom Britton ◽  
Ka Yin Leung ◽  
Pieter Trapman
Keyword(s):  
Real Time ◽  
Random Graph ◽  
Branching Processes ◽  
Large Population ◽  
Graph Representation ◽  
Type Model ◽  
Random Weights ◽  
Stochastic Epidemic ◽  
Special Case ◽  
Large Population Limit

AbstractWe couple a multi-type stochastic epidemic process with a directed random graph, where edges have random weights (traversal times). This random graph representation is used to characterise the fractions of individuals infected by the different types of vertices among all infected individuals in the large population limit. For this characterisation, we rely on the theory of multi-type real-time branching processes. We identify a special case of the two-type model in which the fraction of individuals of a certain type infected by individuals of the same type is maximised among all two-type epidemics approximated by branching processes with the same mean offspring matrix.

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 On the Construction of Some Deterministic and Stochastic Non-Local SIR Models

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2103
Author(s):  
Giacomo Ascione
Keyword(s):  
Deterministic Model ◽  
Large Population ◽  
Epidemic Models ◽  
Fluid Limit ◽  
Sir Epidemic ◽  
Generalized Fractional Calculus ◽  
Stochastic Epidemic ◽  
Non Local ◽  
Stochastic Analog ◽  
Large Population Limit

Fractional-order epidemic models have become widely studied in the literature. Here, we consider the generalization of a simple SIR model in the context of generalized fractional calculus and we study the main features of such model. Moreover, we construct semi-Markov stochastic epidemic models by using time changed continuous time Markov chains, where the parent process is the stochastic analog of a simple SIR epidemic. In particular, we show that, differently from what happens in the classic case, the deterministic model does not coincide with the large population limit of the stochastic one. This loss of fluid limit is then stressed in terms of numerical examples.

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.

REAL-TIME DISPERSIVE REFRACTION WITH ADAPTIVE SPECTRAL MAPPING

2013 ◽  
Vol 22 (06) ◽  
pp. 1360019
Author(s):  
DAMON BLANCHETTE ◽  
EMMANUEL AGU
Keyword(s):  
Real Time ◽  
White Light ◽  
Spectral Mapping ◽  
Mapping Algorithm ◽  
Physically Based ◽  
Refractive Medium ◽  
Interactive Frame ◽  
Screen Space ◽  
Special Case ◽  
Novel Algorithm

Spectral rendering, or the synthesis of images by taking into account the constituent wavelengths of white light, enables the rendering of iridescent colors caused by phenomena such as dispersion, diffraction, interference and scattering. Caustics, the focusing and defocusing of light through a refractive medium, can be interpreted as a special case of dispersion where all the wavelengths travel along the same paths. In this paper we extend Adaptive Caustic Mapping (ACM), a previously proposed caustics mapping algorithm, to handle physically-based dispersion. Because ACM can display caustics in real-time, it is amenable to extension to handle the more general case of dispersion. We also present a novel algorithm for filling in the gaps that occur due to discrete sampling of the spectrum. Our proposed method runs in screen-space, and is fast enough to display plausible dispersion phenomena at real-time and interactive frame rates.

Modelling yeast cell growth using stochastic branching processes

1981 ◽  
Vol 18 (04) ◽  
pp. 799-808 ◽  
Author(s):  
P. J. Green
Keyword(s):  
Cell Growth ◽  
Branching Process ◽  
Deterministic Model ◽  
Branching Processes ◽  
Yeast Cells ◽  
Fixed Duration ◽  
Full Generality ◽  
Asymmetric Growth ◽  
Special Case ◽  
Natural Way

This paper aims to demonstrate that the general Crump–Mode–Jagers branching process may be used in a natural way to model the asymmetric growth of budding yeast cells. The models obtained are generalisations of the deterministic model proposed by Hartwell and Unger (1977): all the results that are derived in that paper may be obtained using branching-process methods, but such methods also apply when account is taken of the biologically obvious fact that the various phases of the cell growth are of random rather than fixed duration. In their full generality, branching processes involve more parameters than can be estimated by experiment, but we present below a special case in which this problem is not likely to arise. A recent paper, Lord and Wheals (1980), discusses more of the biological background than is appropriate here. In the present paper, we show how certain statistical procedures for our model may be developed.

scholarly journals Towards Fully Jitterless Applications: Periodic Scheduling in Multiprocessor MCSs Using a Table-Driven Approach

2020 ◽  
Vol 10 (19) ◽  
pp. 6702
Author(s):  
Eugenia Ana Capota ◽  
Cristina Sorina Stangaciu ◽  
Mihai Victor Micea ◽  
Daniel-Ioan Curiac
Keyword(s):  
Real Time ◽  
Multiprocessor Systems ◽  
Preemptive Scheduling ◽  
Algorithm Performance ◽  
Safety Critical ◽  
Time Table ◽  
Scheduling Method ◽  
Embedded Applications ◽  
Special Case ◽  
Mixed Criticality

In mixed criticality systems (MCSs), the time-triggered scheduling approach focuses on a special case of safety-critical embedded applications which run in a time-triggered environment. Sometimes, for these types of MCSs, perfectly periodical (i.e., jitterless) scheduling for certain critical tasks is needed. In this paper, we propose FENP_MC (Fixed Execution Non-Preemptive Mixed Criticality), a real-time, table-driven, non-preemptive scheduling method specifically adapted to mixed criticality systems which guarantees jitterless execution in a mixed criticality time-triggered environment. We also provide a multiprocessor version, namely, P_FENP_MC (Partitioned Fixed Execution Non-Preemptive Mixed Criticality), using a partitioning heuristic. Feasibility tests are proposed for both uniprocessor and homogenous multiprocessor systems. An analysis of the algorithm performance is presented in terms of success ratio and scheduling jitter by comparing it against a time-triggered and an event-driven method in a non-preemptive context.

scholarly journals Saliva pools for screening of human cytomegalovirus using real-time PCR

2020 ◽  
Author(s):  
Cláudia Fernandes ◽  
Augusta Marques ◽  
Maria de Jesus Chasqueira ◽  
Mónica Cró Braz ◽  
Ana Rute Ferreira ◽  
...  
Keyword(s):  
Real Time ◽  
Human Cytomegalovirus ◽  
Real Time Pcr ◽  
Cost Reduction ◽  
Large Scale ◽  
Hcmv Infection ◽  
Screening Program ◽  
Large Population ◽  
Congenital Infection ◽  
Congenital Hcmv Infection

Abstract Human cytomegalovirus (HCMV) is the leading congenital infection agent in the world. The importance of screening this infection has been debated, as 10–15% of the asymptomatic newborns with HCMV at birth will present late sequelae. The aim of this study was to test the feasibility of using saliva pools from newborns in a screening program for congenital HCMV infection, in two Portuguese hospitals. The screening was based on the use of pools of 10 saliva samples for detection of viral DNA by real-time PCR. Whenever there was a positive pool, the samples were tested individually, and for each positive sample the result was confirmed with a urine sample collected in the first 2 weeks of life. The study involved 1492 newborns. One hundred and fifty pools were screened, with 14 positive results in saliva, but only 10 were confirmed in urine samples, giving a prevalence of congenital HCMV infection in both hospitals of 0.67% (CI95% 0.36 to 1.23%). Conclusion: The overall prevalence of congenital HCMV infection in both hospitals was 0.67%. The use of saliva pools proved to be effective for the screening of this congenital infection, allowing timely screening and confirmation in a large population, with associated cost reduction. What is Known:• Newborn screening for HCMV is desirable.• Saliva is a good and practical sample. What is New:• The feasibility of using saliva pools for a large-scale screening.• The cost reduction of this strategy.

Modelling yeast cell growth using stochastic branching processes

1981 ◽  
Vol 18 (4) ◽  
pp. 799-808 ◽  
Author(s):  
P. J. Green
Keyword(s):  
Cell Growth ◽  
Branching Process ◽  
Deterministic Model ◽  
Branching Processes ◽  
Yeast Cells ◽  
Fixed Duration ◽  
Full Generality ◽  
Asymmetric Growth ◽  
Special Case ◽  
Natural Way

This paper aims to demonstrate that the general Crump–Mode–Jagers branching process may be used in a natural way to model the asymmetric growth of budding yeast cells. The models obtained are generalisations of the deterministic model proposed by Hartwell and Unger (1977): all the results that are derived in that paper may be obtained using branching-process methods, but such methods also apply when account is taken of the biologically obvious fact that the various phases of the cell growth are of random rather than fixed duration. In their full generality, branching processes involve more parameters than can be estimated by experiment, but we present below a special case in which this problem is not likely to arise.A recent paper, Lord and Wheals (1980), discusses more of the biological background than is appropriate here. In the present paper, we show how certain statistical procedures for our model may be developed.

scholarly journals Amplifiers of selection

2015 ◽  
Vol 471 (2181) ◽  
pp. 20150114 ◽  
Author(s):  
B. Adlam ◽  
K. Chatterjee ◽  
M. A. Nowak
Keyword(s):  
Population Structure ◽  
Probability Distribution ◽  
Initial Conditions ◽  
Large Population ◽  
Fixation Probability ◽  
Population Structures ◽  
The Difference ◽  
Large Population Limit

When a new mutant arises in a population, there is a probability it outcompetes the residents and fixes. The structure of the population can affect this fixation probability. Suppressing population structures reduce the difference between two competing variants, while amplifying population structures enhance the difference. Suppressors are ubiquitous and easy to construct, but amplifiers for the large population limit are more elusive and only a few examples have been discovered. Whether or not a population structure is an amplifier of selection depends on the probability distribution for the placement of the invading mutant. First, we prove that there exist only bounded amplifiers for adversarial placement—that is, for arbitrary initial conditions. Next, we show that the Star population structure, which is known to amplify for mutants placed uniformly at random, does not amplify for mutants that arise through reproduction and are therefore placed proportional to the temperatures of the vertices. Finally, we construct population structures that amplify for all mutational events that arise through reproduction, uniformly at random, or through some combination of the two.

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