scholarly journals Stochastic Epidemic Models in Structured Populations Featuring Dynamic Vaccination and Isolation

2007 ◽  
Vol 44 (03) ◽  
pp. 571-585 ◽  
Author(s):  
Frank Ball ◽  
Philip D. O'Neill ◽  
James Pike
Keyword(s):  
Exposure Period ◽  
Structured Populations ◽  
Infectious Period ◽  
Stochastic Comparison ◽  
Threshold Parameter ◽  
Final Size ◽  
Period Distribution ◽  
Comparison Results ◽  
Stochastic Epidemic ◽  
Large Populations

We consider a stochastic model for the spread of an SEIR (susceptible → exposed → infective → removed) epidemic among a population of individuals partitioned into households. The model incorporates both vaccination and isolation in response to the detection of cases. When the infectious period is exponential, we derive an explicit formula for a threshold parameter, and analytic results that enable computation of the probability of the epidemic taking off. These quantities are found to be independent of the exposure period distribution. An approximation for the expected final size of an epidemic that takes off is obtained, evaluated numerically, and found to be reasonably accurate in large populations. When the infectious period is not exponential, but has an increasing hazard rate, we obtain stochastic comparison results in the case where the exposure period is fixed. Our main result shows that as the exposure period increases, both the severity of the epidemic in a single household and the threshold parameter decrease, under certain assumptions concerning isolation. Corresponding results for infectious periods with decreasing hazard rates are also derived.

scholarly journals Stochastic Epidemic Models in Structured Populations Featuring Dynamic Vaccination and Isolation

2007 ◽  
Vol 44 (3) ◽  
pp. 571-585 ◽  
Author(s):  
Frank Ball ◽  
Philip D. O'Neill ◽  
James Pike
Keyword(s):  
Exposure Period ◽  
Structured Populations ◽  
Infectious Period ◽  
Stochastic Comparison ◽  
Threshold Parameter ◽  
Final Size ◽  
Period Distribution ◽  
Comparison Results ◽  
Stochastic Epidemic ◽  
Large Populations

We consider a stochastic model for the spread of an SEIR (susceptible → exposed → infective → removed) epidemic among a population of individuals partitioned into households. The model incorporates both vaccination and isolation in response to the detection of cases. When the infectious period is exponential, we derive an explicit formula for a threshold parameter, and analytic results that enable computation of the probability of the epidemic taking off. These quantities are found to be independent of the exposure period distribution. An approximation for the expected final size of an epidemic that takes off is obtained, evaluated numerically, and found to be reasonably accurate in large populations. When the infectious period is not exponential, but has an increasing hazard rate, we obtain stochastic comparison results in the case where the exposure period is fixed. Our main result shows that as the exposure period increases, both the severity of the epidemic in a single household and the threshold parameter decrease, under certain assumptions concerning isolation. Corresponding results for infectious periods with decreasing hazard rates are also derived.

Other indicators of severity

2012 ◽  
Author(s):  
Odo Diekmann ◽  
Hans Heesterbeek ◽  
Tom Britton
Keyword(s):  
Growth Rate ◽  
Structured Populations ◽  
Infectious Period ◽  
Final Size ◽  
Transmission Parameters ◽  
Contact Rates ◽  
Major Outbreak ◽  
Characteristic Features ◽  
Deterministic Setting ◽  
The Basic Reproduction Number

This chapter is devoted to the initial real-time growth rate r, the probability of a major outbreak, the final size, and the endemic level, in structured populations, with special attention for computational simplifications in the case of separable mixing. Chapter 7 studied the basic reproduction number R₀ for epidemic models in populations manifesting various forms of heterogeneity. It was illustrated that R₀ depends on the transmission parameters, contact rates, the infectious period and on the community structure. The importance of R₀ lies in the fact that an epidemic can, and will in the deterministic setting, take off only if R₀ > 1, a characteristic referred to as supercritical. In a community having births or immigration of susceptibles, this also means that the disease can become endemic. If the parameters and community are such that R₀ < 1 (or R₀ = 1), we are in the subcritical (critical) regime and an epidemic outbreak cannot occur. The chapter examines important supplementary characteristic features and shows how they depend on the different parameters of the model.

scholarly journals Threshold behaviour of emerging epidemics featuring contact tracing

2011 ◽  
Vol 43 (04) ◽  
pp. 1048-1065 ◽  
Author(s):  
Frank G. Ball ◽  
Edward S. Knock ◽  
Philip D. O'Neill
Keyword(s):  
Stochastic Model ◽  
Contact Tracing ◽  
Death Process ◽  
Infectious Period ◽  
Threshold Parameter ◽  
Threshold Behaviour ◽  
Numerical Studies ◽  
Period Distribution ◽  
Extinction Probabilities ◽  
Birth Death

This paper is concerned with a stochastic model for the spread of an epidemic with a contact tracing scheme, in which diagnosed individuals may name some of their infectious contacts, who are then removed if they have not been already. Traced individuals may or may not also be asked to name their own contacts. The epidemic is studied by considering an approximating, modified birth-death process with intersibling dependencies, for which a threshold parameter and expressions from which extinction probabilities may be calculated are derived. When all individuals can name their contacts, it is shown that this threshold parameter depends on the infectious period distribution only through its mean. Numerical studies show that the infectious period distribution choice can have a material effect on the threshold behaviour of an epidemic, while the dependencies help reduce spread.

scholarly journals How big is an outbreak likely to be? Methods for epidemic final-size calculation

2013 ◽  
Vol 469 (2150) ◽  
pp. 20120436 ◽  
Author(s):  
Thomas House ◽  
Joshua V. Ross ◽  
David Sirl
Keyword(s):  
Infectious Disease ◽  
Mass Function ◽  
Probability Mass Function ◽  
Final Size ◽  
Numerical Efficiency ◽  
Stochastic Epidemic ◽  
Large Populations ◽  
Probability Mass ◽  
Computationally Intensive ◽  
The Moment

Epidemic models have become a routinely used tool to inform policy on infectious disease. A particular interest at the moment is the use of computationally intensive inference to parametrize these models. In this context, numerical efficiency is critically important. We consider methods for evaluating the probability mass function of the total number of infections over the course of a stochastic epidemic, with a focus on homogeneous finite populations, but also considering heterogeneous and large populations. Relevant methods are reviewed critically, with existing and novel extensions also presented. We provide code in M atlab and a systematic comparison of numerical efficiency.

scholarly journals Threshold behaviour of emerging epidemics featuring contact tracing

2011 ◽  
Vol 43 (4) ◽  
pp. 1048-1065 ◽  
Author(s):  
Frank G. Ball ◽  
Edward S. Knock ◽  
Philip D. O'Neill
Keyword(s):  
Stochastic Model ◽  
Contact Tracing ◽  
Death Process ◽  
Infectious Period ◽  
Threshold Parameter ◽  
Threshold Behaviour ◽  
Numerical Studies ◽  
Period Distribution ◽  
Extinction Probabilities ◽  
Birth Death

This paper is concerned with a stochastic model for the spread of an epidemic with a contact tracing scheme, in which diagnosed individuals may name some of their infectious contacts, who are then removed if they have not been already. Traced individuals may or may not also be asked to name their own contacts. The epidemic is studied by considering an approximating, modified birth-death process with intersibling dependencies, for which a threshold parameter and expressions from which extinction probabilities may be calculated are derived. When all individuals can name their contacts, it is shown that this threshold parameter depends on the infectious period distribution only through its mean. Numerical studies show that the infectious period distribution choice can have a material effect on the threshold behaviour of an epidemic, while the dependencies help reduce spread.

scholarly journals Comparison Results for GARCH Processes

2014 ◽  
Vol 51 (3) ◽  
pp. 685-698
Author(s):  
Fabio Bellini ◽  
Franco Pellerey ◽  
Carlo Sgarra ◽  
Salimeh Yasaei Sekeh
Keyword(s):  
Stochastic Orders ◽  
Stochastic Comparison ◽  
Convex Order ◽  
Comparison Results ◽  
Garch Processes ◽  
Garch Process

We consider the problem of stochastic comparison of general GARCH-like processes for different parameters and different distributions of the innovations. We identify several stochastic orders that are propagated from the innovations to the GARCH process itself, and we discuss their interpretations. We focus on the convex order and show that in the case of symmetric innovations it is also propagated to the cumulated sums of the GARCH process. More generally, we discuss multivariate comparison results related to the multivariate convex and supermodular orders. Finally, we discuss ordering with respect to the parameters in the GARCH(1, 1) case.

Stochastic comparison of repairable systems by coupling

1998 ◽  
Vol 35 (2) ◽  
pp. 348-370 ◽  
Author(s):  
Günter Last ◽  
Ryszard Szekli
Keyword(s):  
Point Processes ◽  
Stochastic Comparison ◽  
Repairable Systems ◽  
Imperfect Repair ◽  
Coupling Methods ◽  
Comparison Results ◽  
Special Cases ◽  
Repair Models

Stochastic comparison results for replacement policies are shown in this paper using the formalism of point processes theory. At each failure moment a repair is allowed. It is performed with a random degree of repair including (as special cases) perfect, minimal and imperfect repair models. Results for such repairable systems with schemes of planned replacements are also shown. The results are obtained by coupling methods for point processes.

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