A Stochastic Differential Equation SIS Epidemic Model

Gray, Alison; Greenhalgh, David; Hu, Liangjian; Mao, Xuerong; Pan, Jiafeng

doi:10.1137/10081856x

Cited by 622 publications

(567 citation statements)

References 26 publications

(45 reference statements)

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“…In relation to the theme of this paper, we particularly want to note the paper [6] which proves a stability result allowing for R 0 to exceed the value 1. The current paper makes a useful contribution to understanding the disease-free equilibrium of the given sde model of an SEIR disease.…”

Section: Resultsmentioning

confidence: 99%

“…There are models in which the transmission rate from susceptible to infected is perturbed such as in the Refs. [6,16,20] and others. We propose a model in which stochasticity is directly imposed on all the classes other than the class of susceptibles.…”

Section: The Seir Modelmentioning

confidence: 99%

“…Various approaches have been taken towards 2 incorporating random phenomena of nature into epidemiological models. One such approach is to utilize stochastic differential equations, and in the paper [6] of Gray et al such models are referred to as sde models. Also, many different disease types have been modeled using sde's.…”

Section: Introductionmentioning

confidence: 99%

“…[13] for instance. It is also illustrated in the paper [6] for the case of disease-free equilibrium of an SIS model and in Ref. [14].…”

Section: Introductionmentioning

confidence: 99%

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Stability of an SEIR epidemic model with independent stochastic perturbations

Witbooi

2013

Physica A: Statistical Mechanics and its Applications

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Stability of an SEIR epidemic model with independent stochastic perturbationsPeter J. Witbooi AbstractFor an epidemic model of the type mentioned, we prove a theorem on almost sure exponential stability of the disease-free equilibrium. For small values of the diffusion parameter, σ , we describe the stability of the disease free equilibrium point in terms of an appropriate analogue, R σ , of the basic reproduction number R 0 of the deterministic special case. Whenever σ > 0 then R σ < R 0 . For small values of σ , the stability theorem guarantees almost sure exponential stability whenever R σ < 1. We also discuss the effect of increasing σ .

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Section: Resultsmentioning

confidence: 99%

Section: The Seir Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…[13] for instance. It is also illustrated in the paper [6] for the case of disease-free equilibrium of an SIS model and in Ref. [14].…”

Section: Introductionmentioning

confidence: 99%

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Stability of an SEIR epidemic model with independent stochastic perturbations

Witbooi

2013

Physica A: Statistical Mechanics and its Applications

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“…The parameters β, α, λ are all nonnegative constants and Λ, µ are positive constants. Recently, authors of [4,6,21] have done much research and have obtained plenty of significant conclusions for system (1.1). They set up the threshold condition R * , which determines disease extinction or permanence under stochastic perturbation, where…”

Section: βS(t)i(t)mentioning

confidence: 99%

Nonlinear stochastic analysis for a stochastic SIS epidemic model

Li¹,

Meng²,

Cui³

2017

J. Nonlinear Sci. Appl.

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This paper considers a stochastic Susceptible-Infected-Susceptible (SIS) epidemic model with nonlinear saturated incidence. The threshold conditions for disease extinction and stochastic permanence are obtained by using nonlinear stochastic analysis for Feller's test and the canonical probability method. Consequently, this improves and extends some previous results obtained by using Lyapunov method. A series of numerical simulations are carried out to illustrate our theoretical findings.

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A Bayesian SIRS model for the analysis of respiratory syncytial virus in the region of Valencia, Spain

Corberán-Vallet

Santonja

2014

Biometrical J

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We present a Bayesian stochastic susceptible-infected-recovered-susceptible (SIRS) model in discrete time to understand respiratory syncytial virus dynamics in the region of Valencia, Spain. A SIRS model based on ordinary differential equations has also been proposed to describe RSV dynamics in the region of Valencia. However, this continuous-time deterministic model is not suitable when the initial number of infected individuals is small. Stochastic epidemic models based on a probability of disease transmission provide a more natural description of the spread of infectious diseases. In addition, by allowing the transmission rate to vary stochastically over time, the proposed model provides an improved description of RSV dynamics. The Bayesian analysis of the model allows us to calculate both the posterior distribution of the model parameters and the posterior predictive distribution, which facilitates the computation of point forecasts and prediction intervals for future observations.

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A Stochastic Differential Equation SIS Epidemic Model

Cited by 622 publications

References 26 publications

Stability of an SEIR epidemic model with independent stochastic perturbations

Stability of an SEIR epidemic model with independent stochastic perturbations

Nonlinear stochastic analysis for a stochastic SIS epidemic model

A Bayesian SIRS model for the analysis of respiratory syncytial virus in the region of Valencia, Spain

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