Limit theorems for the total size of a spatial epidemic

1997 ◽  
Vol 34 (3) ◽  
pp. 698-710 ◽  
Author(s):  
Håkan Andersson ◽  
Boualem Djehiche
Keyword(s):  
Asymptotic Behaviour ◽  
Epidemic Model ◽  
Limit Theorems ◽  
Total Size ◽  
Spatial Epidemic Model ◽  
Spatial Epidemic ◽  
Number Of Individuals ◽  
General Stochastic

We study the long-term behaviour of a sequence of multitype general stochastic epidemics, converging in probability to a deterministic spatial epidemic model, proposed by D. G. Kendall. More precisely, we use branching and deterministic approximations in order to study the asymptotic behaviour of the total size of the epidemics as the number of types and the number of individuals of each type both grow to infinity.

Limit theorems for the total size of a spatial epidemic

1997 ◽  
Vol 34 (03) ◽  
pp. 698-710
Author(s):  
Håkan Andersson ◽  
Boualem Djehiche
Keyword(s):  
Asymptotic Behaviour ◽  
Epidemic Model ◽  
Limit Theorems ◽  
Total Size ◽  
Spatial Epidemic Model ◽  
Spatial Epidemic ◽  
Number Of Individuals ◽  
General Stochastic

We study the long-term behaviour of a sequence of multitype general stochastic epidemics, converging in probability to a deterministic spatial epidemic model, proposed by D. G. Kendall. More precisely, we use branching and deterministic approximations in order to study the asymptotic behaviour of the total size of the epidemics as the number of types and the number of individuals of each type both grow to infinity.

Asymptotic analysis of the general stochastic epidemic with variable infectious periods

2001 ◽  
Vol 38 (01) ◽  
pp. 18-35 ◽  
Author(s):  
A. N. Startsev
Keyword(s):  
Asymptotic Analysis ◽  
Asymptotic Behaviour ◽  
Size Distribution ◽  
Random Variables ◽  
Independent Random Variables ◽  
Boundary Crossing ◽  
Total Size ◽  
Stochastic Epidemic ◽  
General Stochastic

A generalisation of the classical general stochastic epidemic within a closed, homogeneously mixing population is considered, in which the infectious periods of infectives follow i.i.d. random variables having an arbitrary but specified distribution. The asymptotic behaviour of the total size distribution for the epidemic as the initial numbers of susceptibles and infectives tend to infinity is investigated by generalising the construction of Sellke and reducing the problem to a boundary crossing problem for sums of independent random variables.

scholarly journals Parameter Scaling for Epidemic Size in a Spatial Epidemic Model with Mobile Individuals

PLoS ONE ◽  
2016 ◽  
Vol 11 (12) ◽  
pp. e0168127 ◽  
Author(s):  
Chiyori T. Urabe ◽  
Gouhei Tanaka ◽  
Kazuyuki Aihara ◽  
Masayasu Mimura
Keyword(s):  
Epidemic Model ◽  
Epidemic Size ◽  
Spatial Epidemic Model ◽  
Spatial Epidemic

scholarly journals Chaos in a spatial epidemic model

2009 ◽  
Vol 19 (4) ◽  
pp. 1656-1685 ◽  
Author(s):  
Rick Durrett ◽  
Daniel Remenik
Keyword(s):  
Epidemic Model ◽  
Spatial Epidemic Model ◽  
Spatial Epidemic

Asymptotic analysis of the general stochastic epidemic with variable infectious periods

2001 ◽  
Vol 38 (1) ◽  
pp. 18-35 ◽  
Author(s):  
A. N. Startsev
Keyword(s):  
Asymptotic Analysis ◽  
Asymptotic Behaviour ◽  
Size Distribution ◽  
Random Variables ◽  
Independent Random Variables ◽  
Boundary Crossing ◽  
Total Size ◽  
Stochastic Epidemic ◽  
General Stochastic

A generalisation of the classical general stochastic epidemic within a closed, homogeneously mixing population is considered, in which the infectious periods of infectives follow i.i.d. random variables having an arbitrary but specified distribution. The asymptotic behaviour of the total size distribution for the epidemic as the initial numbers of susceptibles and infectives tend to infinity is investigated by generalising the construction of Sellke and reducing the problem to a boundary crossing problem for sums of independent random variables.

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