Stochastic Multigroup Epidemic Models: Duration and Final Size

2019 ◽  
pp. 483-507
Author(s):  
Aadrita Nandi ◽  
Linda J. S. Allen
Keyword(s):  
Epidemic Models ◽  
Final Size

scholarly journals SPATIAL HETEROGENEITY IN SIMPLE DETERMINISTIC SIR MODELS ASSESSED ECOLOGICALLY

2012 ◽  
Vol 54 (1-2) ◽  
pp. 23-36 ◽  
Author(s):  
E. K. WATERS ◽  
H. S. SIDHU ◽  
G. N. MERCER
Keyword(s):  
Infectious Disease ◽  
Spatial Heterogeneity ◽  
Disease Transmission ◽  
Herd Immunity ◽  
Epidemic Models ◽  
Final Size ◽  
Infectious Disease Transmission ◽  
Epidemic Dynamics ◽  
Mean Crowding ◽  
Rate Of Movement

AbstractPatchy or divided populations can be important to infectious disease transmission. We first show that Lloyd’s mean crowding index, an index of patchiness from ecology, appears as a term in simple deterministic epidemic models of the SIR type. Using these models, we demonstrate that the rate of movement between patches is crucial for epidemic dynamics. In particular, there is a relationship between epidemic final size and epidemic duration in patchy habitats: controlling inter-patch movement will reduce epidemic duration, but also final size. This suggests that a strategy of quarantining infected areas during the initial phases of a virulent epidemic might reduce epidemic duration, but leave the population vulnerable to future epidemics by inhibiting the development of herd immunity.

scholarly journals Coupling of Two SIR Epidemic Models with Variable Susceptibilities and Infectivities

2007 ◽  
Vol 44 (01) ◽  
pp. 41-57 ◽  
Author(s):  
Peter Neal
Keyword(s):  
Size Distribution ◽  
Random Graph ◽  
Epidemic Model ◽  
Epidemic Models ◽  
Final Size ◽  
Sir Epidemic ◽  
Novel Approach ◽  
Stochastic Epidemic ◽  
Sir Epidemic Models ◽  
Variable Susceptibility

The variable generalised stochastic epidemic model, which allows for variability in both the susceptibilities and infectivities of individuals, is analysed. A very different epidemic model which exhibits variable susceptibility and infectivity is the random-graph epidemic model. A suitable coupling of the two epidemic models is derived which enables us to show that, whilst the epidemics are very different in appearance, they have the same asymptotic final size distribution. The coupling provides a novel approach to studying random-graph epidemic models.

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.

scholarly journals Solvability of implicit final size equations for SIR epidemic models

2016 ◽  
Vol 282 ◽  
pp. 181-190 ◽  
Author(s):  
Subekshya Bidari ◽  
Xinying Chen ◽  
Daniel Peters ◽  
Dylanger Pittman ◽  
Péter L. Simon
Keyword(s):  
Epidemic Models ◽  
Final Size ◽  
Sir Epidemic ◽  
Sir Epidemic Models

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.

Poisson approximation for some epidemic models

1990 ◽  
Vol 27 (3) ◽  
pp. 479-490 ◽  
Author(s):  
Frank Ball ◽  
A. D. Barbour
Keyword(s):  
Limit Theorem ◽  
Directed Graph ◽  
Poisson Approximation ◽  
Epidemic Models ◽  
Final Size ◽  
Stochastic Epidemic ◽  
Order Of Magnitude ◽  
Poisson Limit ◽  
General Stochastic

The Daniels' Poisson limit theorem for the final size of a severe general stochastic epidemic is extended to the Martin-Löf epidemic, and an order of magnitude for the error in the approximation is also given. The argument consists largely of showing that the number of survivors of a severe epidemic is essentially the same as the number of isolated vertices in a random directed graph. Poisson approximation for the latter quantity is proved using the Stein–Chen method and a suitable coupling.

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