Some comparison results for multitype epidemic models

1994 ◽  
Vol 31 (1) ◽  
pp. 9-21 ◽  
Author(s):  
Damian Clancy
Keyword(s):  
Epidemic Models ◽  
Current Group ◽  
Total Size ◽  
Comparison Results

We consider a model for the spread of an epidemic through a population divided into m groups, in which infectives move from group to group and infect only within their current group. For both deterministic and stochastic versions of this model, the effect on the total size of the epidemic of varying the speed with which infectives move between groups is considered. We also compare the distribution of the total size of this model with that of a suitably matched model in which infectives cannot move between groups, but are able to infect outside their own group.

Some comparison results for multitype epidemic models

1994 ◽  
Vol 31 (01) ◽  
pp. 9-21 ◽  
Author(s):  
Damian Clancy
Keyword(s):  
Epidemic Models ◽  
Current Group ◽  
Total Size ◽  
Comparison Results

We consider a model for the spread of an epidemic through a population divided into m groups, in which infectives move from group to group and infect only within their current group. For both deterministic and stochastic versions of this model, the effect on the total size of the epidemic of varying the speed with which infectives move between groups is considered. We also compare the distribution of the total size of this model with that of a suitably matched model in which infectives cannot move between groups, but are able to infect outside their own group.

A note on the total size distribution of carrier-borne epidemic models

1990 ◽  
Vol 27 (04) ◽  
pp. 908-912
Author(s):  
Frank Ball
Keyword(s):  
Size Distribution ◽  
Epidemic Models ◽  
Coupling Method ◽  
Total Size

The coupling method of Ball (1986) is extended to carrier-borne epidemics, thus providing a new proof of a result of Daniels (1972) concerning the total size distribution of Downton's stochastic carrier-borne epidemic. The generalization to multipopulation carrier-borne epidemics is immediate.

A note on the total size distribution of epidemic models

1986 ◽  
Vol 23 (03) ◽  
pp. 832-836 ◽  
Author(s):  
Frank Ball
Keyword(s):  
Size Distribution ◽  
Epidemic Models ◽  
Total Size ◽  
Stochastic Epidemic ◽  
General Stochastic

A simple coupling argument is used to obtain a new proof of a result of Daniels (1967) concerning the total size distribution of the general stochastic epidemic. The proof admits a straightforward generalisation to multipopulation epidemics and indicates that similar results are unlikely to be available for epidemics with non-exponential infectious periods.

The final size and severity of a generalised stochastic multitype epidemic model

1993 ◽  
Vol 25 (4) ◽  
pp. 721-736 ◽  
Author(s):  
Frank Ball ◽  
Damian Clancy
Keyword(s):  
Stochastic Model ◽  
Epidemic Model ◽  
Exact Results ◽  
Final Size ◽  
Asymptotic Results ◽  
Current Group ◽  
Total Size ◽  
Original Group

We consider a stochastic model for the spread of an epidemic amongst a population split into m groups, in which infectives move among the groups and contact susceptibles at a rate which depends upon the infective's original group, its current group, and the group of the susceptible. The distributions of total size and total area under the trajectory of infectives for such epidemics are analysed. We derive exact results in terms of multivariate Gontcharoff polynomials by treating our model as a multitype collective Reed–Frost process and slightly adapting the results of Picard and Lefèvre (1990). We also derive asymptotic results, as each of the group sizes becomes large, by generalising the method of Scalia-Tomba (1985), (1990).

A note on the total size distribution of epidemic models

1986 ◽  
Vol 23 (3) ◽  
pp. 832-836 ◽  
Author(s):  
Frank Ball
Keyword(s):  
Size Distribution ◽  
Epidemic Models ◽  
Total Size ◽  
Stochastic Epidemic ◽  
General Stochastic

A simple coupling argument is used to obtain a new proof of a result of Daniels (1967) concerning the total size distribution of the general stochastic epidemic. The proof admits a straightforward generalisation to multipopulation epidemics and indicates that similar results are unlikely to be available for epidemics with non-exponential infectious periods.

The final size and severity of a generalised stochastic multitype epidemic model

1993 ◽  
Vol 25 (04) ◽  
pp. 721-736 ◽  
Author(s):  
Frank Ball ◽  
Damian Clancy
Keyword(s):  
Stochastic Model ◽  
Epidemic Model ◽  
Exact Results ◽  
Final Size ◽  
Asymptotic Results ◽  
Current Group ◽  
Total Size ◽  
Original Group

We consider a stochastic model for the spread of an epidemic amongst a population split into m groups, in which infectives move among the groups and contact susceptibles at a rate which depends upon the infective's original group, its current group, and the group of the susceptible. The distributions of total size and total area under the trajectory of infectives for such epidemics are analysed. We derive exact results in terms of multivariate Gontcharoff polynomials by treating our model as a multitype collective Reed–Frost process and slightly adapting the results of Picard and Lefèvre (1990). We also derive asymptotic results, as each of the group sizes becomes large, by generalising the method of Scalia-Tomba (1985), (1990).

A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models

1986 ◽  
Vol 18 (2) ◽  
pp. 289-310 ◽  
Author(s):  
Frank Ball
Keyword(s):  
Probabilistic Approach ◽  
Heterogeneous Population ◽  
Epidemic Models ◽  
Infectious Period ◽  
Unified Approach ◽  
Total Size ◽  
Epidemic Process ◽  
Stochastic Epidemic ◽  
General Stochastic

We provide a unified probabilistic approach to the distribution of total size and total area under the trajectory of infectives for a general stochastic epidemic with any specified distribution of the infectious period. The key tool is a Wald&s identity for the epidemic process. The generalisation of our results to epidemics spreading amongst a heterogeneous population is straightforward.

A note on the total size distribution of carrier-borne epidemic models

1990 ◽  
Vol 27 (4) ◽  
pp. 908-912 ◽  
Author(s):  
Frank Ball
Keyword(s):  
Size Distribution ◽  
Epidemic Models ◽  
Coupling Method ◽  
Total Size

The coupling method of Ball (1986) is extended to carrier-borne epidemics, thus providing a new proof of a result of Daniels (1972) concerning the total size distribution of Downton's stochastic carrier-borne epidemic. The generalization to multipopulation carrier-borne epidemics is immediate.

A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models

1986 ◽  
Vol 18 (02) ◽  
pp. 289-310 ◽  
Author(s):  
Frank Ball
Keyword(s):  
Probabilistic Approach ◽  
Heterogeneous Population ◽  
Epidemic Models ◽  
Infectious Period ◽  
Unified Approach ◽  
Total Size ◽  
Epidemic Process ◽  
Stochastic Epidemic ◽  
General Stochastic

We provide a unified probabilistic approach to the distribution of total size and total area under the trajectory of infectives for a general stochastic epidemic with any specified distribution of the infectious period. The key tool is a Wald&s identity for the epidemic process. The generalisation of our results to epidemics spreading amongst a heterogeneous population is straightforward.

Perceptions of Stuttering of Different Age Groups

2019 ◽  
Vol 4 (6) ◽  
pp. 1311-1315
Author(s):  
Sergey M. Kondrashov ◽  
John A. Tetnowski
Keyword(s):  
Age Groups ◽  
School Age Children ◽  
Clinical Implications ◽  
School Age ◽  
Fourth Edition ◽  
Self Perception ◽  
Behavioral Measures ◽  
Self Rating ◽  
Comparison Results ◽  
Subject Pool

Purpose The purpose of this study was to assess the perceptions of stuttering of school-age children who stutter and those of adults who stutter through the use of the same tools that could be commonly used by clinicians. Method Twenty-three participants across various ages and stuttering severity were administered both the Stuttering Severity Instrument–Fourth Edition (SSI-4; Riley, 2009 ) and the Wright & Ayre Stuttering Self-Rating Profile ( Wright & Ayre, 2000 ). Comparisons were made between severity of behavioral measures of stuttering made by the SSI-4 and by age (child/adult). Results Significant differences were obtained for the age comparison but not for the severity comparison. Results are explained in terms of the correlation between severity equivalents of the SSI-4 and the Wright & Ayre Stuttering Self-Rating Profile scores, with clinical implications justifying multi-aspect assessment. Conclusions Clinical implications indicate that self-perception and impact of stuttering must not be assumed and should be evaluated for individual participants. Research implications include further study with a larger subject pool and various levels of stuttering severity.

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