An Sir Epidemic Model on a Population with Random Network and Household Structure, and Several Types of Individuals

Ball, Frank; Sirl, David

doi:10.1017/s0001867800005450

Cited by 6 publications

(2 citation statements)

References 35 publications

(26 reference statements)

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“…On the other hand, stochastic SIR models have been applied to simulate and predict the spatiotemporal diffusion of infectious diseases (Hufnagel et al, 2004;Cressie and Wikle, 2011;Ball and Sirl, 2012;Ji et al, 2012;de Souza et al, 2013;Zhang et al, 2013). This modeling, based on a consideration of stochastic differential equations, characterizes not only the spatiotemporal pattern of disease spread, but also the heteroscedastic variance pattern across space and time.…”

Section: Discussionmentioning

confidence: 99%

An online spatiotemporal prediction model for dengue fever epidemic inKaohsiung (Taiwan)

Angulo

Cheng

et al. 2014

Biometrical J

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The emergence and re-emergence of disease epidemics is a complex question that may be influenced by diverse factors, including the space-time dynamics of human populations, environmental conditions, and associated uncertainties. This study proposes a stochastic framework to integrate space-time dynamics in the form of a Susceptible-Infected-Recovered (SIR) model, together with uncertain disease observations, into a Bayesian maximum entropy (BME) framework. The resulting model (BME-SIR) can be used to predict space-time disease spread. Specifically, it was applied to obtain a space-time prediction of the dengue fever (DF) epidemic that took place in Kaohsiung City (Taiwan) during 2002. In implementing the model, the SIR parameters were continually updated and information on new cases of infection was incorporated. The results obtained show that the proposed model is rigorous to user-specified initial values of unknown model parameters, that is, transmission and recovery rates. In general, this model provides a good characterization of the spatial diffusion of the DF epidemic, especially in the city districts proximal to the location of the outbreak. Prediction performance may be affected by various factors, such as virus serotypes and human intervention, which can change the space-time dynamics of disease diffusion. The proposed BME-SIR disease prediction model can provide government agencies with a valuable reference for the timely identification, control, and prevention of DF spread in space and time.

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Section: Discussionmentioning

confidence: 99%

An online spatiotemporal prediction model for dengue fever epidemic inKaohsiung (Taiwan)

Angulo

Cheng

et al. 2014

Biometrical J

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“…[7,8]. In order to increase heterogeneity, the household structure of the population is also taken into account in [6], and global contacts are made through the edges of a random graph with a given degree distribution in [9], where household structure is also considered.…”

Section: Introductionmentioning

confidence: 99%

Solvability of implicit final size equations for SIR epidemic models

Bidari¹,

Chen²,

Peters³

et al. 2016

Mathematical Biosciences

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Final epidemic size relations play a central role in mathematical epidemiology. These can be written in the form of an implicit equation which is not analytically solvable in most of the cases. While final size relations were derived for several complex models, including multiple infective stages and models in which the durations of stages are arbitrarily distributed, the solvability of those implicit equations have been less studied. In this paper the SIR homogeneous mean-field and pairwise models and the heterogeneous mean-field model are studied. It is proved that the implicit equation for the final epidemic size has a unique solution, and that through writing the implicit equation as a fixed point equation in a suitable form, the iteration of the fixed point equation converges to the unique solution. The Markovian SIR epidemic model on finite networks is also studied by using the generation-based approach. Explicit analytic formulas are derived for the final size distribution for line and star graphs of arbitrary size. Iterative formulas for the final size distribution enable us to study the accuracy of mean-field approximations for the complete graph.

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Evaluation of vaccination strategies for SIR epidemics on random networks incorporating household structure

Ball

Sirl

2017

J. Math. Biol.

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This paper is concerned with the analysis of vaccination strategies in a stochastic susceptible infected removed model for the spread of an epidemic amongst a population of individuals with a random network of social contacts that is also partitioned into households. Under various vaccine action models, we consider both household-based vaccination schemes, in which the way in which individuals are chosen for vaccination depends on the size of the households in which they reside, and acquaintance vaccination, which targets individuals of high degree in the social network. For both types of vaccination scheme, assuming a large population with few initial infectives, we derive a threshold parameter which determines whether or not a large outbreak can occur and also the probability of a large outbreak and the fraction of the population infected by a large outbreak. The performance of these schemes is studied numerically, focusing on the influence of the household size distribution and the degree distribution of the social network. We find that acquaintance vaccination can significantly outperform the best household-based scheme if the degree distribution of the social network is heavy-tailed. For household-based schemes, when the vaccine coverage is insufficient to prevent a major outbreak and the vaccine is imperfect, we find situations in which both the probability and size of a major outbreak under the scheme which minimises the threshold parameter are larger than in the scheme which maximises the threshold parameter.

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An Sir Epidemic Model on a Population with Random Network and Household Structure, and Several Types of Individuals

Cited by 6 publications

References 35 publications

An online spatiotemporal prediction model for dengue fever epidemic inKaohsiung (Taiwan)

An online spatiotemporal prediction model for dengue fever epidemic inKaohsiung (Taiwan)

Solvability of implicit final size equations for SIR epidemic models

Evaluation of vaccination strategies for SIR epidemics on random networks incorporating household structure

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