Stochastic epidemic models with random environment: quasi-stationarity, extinction and final size

2012 ◽  
Vol 67 (4) ◽  
pp. 799-831 ◽  
Author(s):  
J. R. Artalejo ◽  
A. Economou ◽  
M. J. Lopez-Herrero
Keyword(s):  
Random Environment ◽  
Epidemic Models ◽  
Final Size ◽  
Stochastic Epidemic Models ◽  
Stochastic Epidemic

The distribution of general final state random variables for stochastic epidemic models

1999 ◽  
Vol 36 (2) ◽  
pp. 473-491 ◽  
Author(s):  
Frank Ball ◽  
Philip O'Neill
Keyword(s):  
Random Variables ◽  
Epidemic Models ◽  
Exact Results ◽  
Final Size ◽  
Single Population ◽  
Final State ◽  
Stochastic Epidemic Models ◽  
Basic Model ◽  
Stochastic Epidemic ◽  
Quantities Of Interest

In this paper we introduce the notion of general final state random variables for generalized epidemic models. These random variables are defined as sums over all ultimately infected individuals of random quantities of interest associated with an individual; examples include final severity. By exploiting a construction originally due to Sellke (1983), exact results concerning the final size and general final state random variables are obtained in terms of Gontcharoff polynomials. In particular, our approach highlights the way in which these polynomials arise via simple probabilistic arguments. For ease of exposition we focus initially upon the single-population case before extending our arguments to multi-population epidemics and other variants of our basic model.

The distribution of general final state random variables for stochastic epidemic models

1999 ◽  
Vol 36 (02) ◽  
pp. 473-491 ◽  
Author(s):  
Frank Ball ◽  
Philip O'Neill
Keyword(s):  
Random Variables ◽  
Epidemic Models ◽  
Exact Results ◽  
Final Size ◽  
Single Population ◽  
Final State ◽  
Stochastic Epidemic Models ◽  
Basic Model ◽  
Stochastic Epidemic ◽  
Quantities Of Interest

In this paper we introduce the notion of general final state random variables for generalized epidemic models. These random variables are defined as sums over all ultimately infected individuals of random quantities of interest associated with an individual; examples include final severity. By exploiting a construction originally due to Sellke (1983), exact results concerning the final size and general final state random variables are obtained in terms of Gontcharoff polynomials. In particular, our approach highlights the way in which these polynomials arise via simple probabilistic arguments. For ease of exposition we focus initially upon the single-population case before extending our arguments to multi-population epidemics and other variants of our basic model.

LOOKING FOR A COMMON STRUCTURE IN STANDARD S-I-R EPIDEMIC MODELS

1995 ◽  
Vol 03 (03) ◽  
pp. 821-831
Author(s):  
PHILIPPE PICARD ◽  
CLAUDE LEFÈVRE
Keyword(s):  
Epidemic Models ◽  
The Other ◽  
Final Size ◽  
Stochastic Epidemic Models ◽  
Common Structure ◽  
Stochastic Epidemic

In classical S-I-R stochastic epidemic models, the formulae giving the distribution of the final size of the epidemic are very robust from one model to the other. This shows that these models, even if they may look different, share a common structure. In the present paper we prove that all the associated final size laws may be expressed in terms of parameters qk, where qk represents the probability that any given set of k susceptibles does not get infected from any given infective. Some consequences and methods of study for S-I-R models in general follow from this characteristic.

scholarly journals Efficient Data Augmentation for Fitting Stochastic Epidemic Models to Prevalence Data

2017 ◽  
Vol 26 (4) ◽  
pp. 918-929 ◽  
Author(s):  
Jonathan Fintzi ◽  
Xiang Cui ◽  
Jon Wakefield ◽  
Vladimir N. Minin
Keyword(s):  
Data Augmentation ◽  
Epidemic Models ◽  
Prevalence Data ◽  
Stochastic Epidemic Models ◽  
Stochastic Epidemic ◽  
Efficient Data

On interarrival times in simple stochastic epidemic models

1982 ◽  
Vol 19 (4) ◽  
pp. 835-841
Author(s):  
Grace Yang ◽  
C. L. Chiang
Keyword(s):  
Probability Distributions ◽  
Asymptotic Distributions ◽  
Epidemic Models ◽  
Stochastic Epidemic Models ◽  
Stochastic Epidemic ◽  
Interarrival Times

The probability distributions of the size and the duration of simple stochastic epidemic models are well known. However, in most instances, the solutions are too complicated to be of practical use. In this note, interarrival times of the infectives are utilized to study asymptotic distributions of the duration of the epidemic for a class of simple epidemic models. A brief summary of the results on simple epidemic models in terms of interarrival times is included.

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