The Behavior of an SIR Epidemic Model with Stochastic Perturbation

Ji, Chunyan; Jiang, Daqing; Shi, Ning

doi:10.1080/07362994.2012.684319

Cited by 110 publications

(50 citation statements)

References 26 publications

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“…Recently, the SIR epidemic model has been widely analyzed in the literature due to its theoretical and practical significance and the study of the model will continue to be one of the dominant themes in mathematical epidemiology (see e.g. [2,3,4,5]). The following model is one of the most classical SIR epidemic models…”

Section: Introductionmentioning

confidence: 99%

Periodic solution and stationary distribution of stochastic SIR epidemic models with higher order perturbation

Jiang

Hayat

et al. 2017

Physica A: Statistical Mechanics and its Applications

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Section: Introductionmentioning

confidence: 99%

Periodic solution and stationary distribution of stochastic SIR epidemic models with higher order perturbation

Jiang

Hayat

et al. 2017

Physica A: Statistical Mechanics and its Applications

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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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“…Kermack [5]. The model is simple and has been widely used so far, for instance, in multigroup epidemic modeling [6], online social network dynamics [7], the model adopting the delay term [8], stochastic model [6,9,10], vaccination strategy [11,12]. In this model, the population is divided into susceptible S(t), infected I(t), and removed R(t) individuals at time t. The governing ordinary differential equations for the SIR model are as follows:…”

Section: The Mathematical Modelmentioning

confidence: 99%

The daily computed weighted averaging basic reproduction number R0,k,ωn for MERS-CoV in South Korea

Jeong

Lee

Choi

et al. 2016

Physica A: Statistical Mechanics and its Applications

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h i g h l i g h t s• We propose the daily basic reproduction number for MERS-CoV in South Korea.• We use an SIR model with piecewise constant contact and removed rates.• We apply the explicit Euler's method for the solution of the SIR model. • We use nonlinear least-square fitting procedure for finding the best parameters. a b s t r a c tIn this paper, we propose the daily computed weighted averaging basic reproduction number R n 0,k,ω for Middle East respiratory syndrome coronavirus (MERS-CoV) outbreak in South Korea, May to July 2015. We use an SIR model with piecewise constant parameters β (contact rate) and γ (removed rate). We use the explicit Euler's method for the solution of the SIR model and a nonlinear least-square fitting procedure for finding the best parameters. In R n 0,k,ω , the parameters n, k, and w denote days from a reference date, the number of days in averaging, and a weighting factor, respectively. We perform a series of numerical experiments and compare the results with the real-world data. In particular, using the predicted reproduction number based on the previous two consecutive reproduction numbers, we can predict the future behavior of the reproduction number.

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The Behavior of an SIR Epidemic Model with Stochastic Perturbation

Cited by 110 publications

References 26 publications

Periodic solution and stationary distribution of stochastic SIR epidemic models with higher order perturbation

Periodic solution and stationary distribution of stochastic SIR epidemic models with higher order perturbation

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

The daily computed weighted averaging basic reproduction number R0,k,ωn for MERS-CoV in South Korea

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