Stability of SIRS system with random perturbations

Lu, Qiuying

doi:10.1016/j.physa.2009.05.036

Cited by 122 publications

(58 citation statements)

References 9 publications

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“…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%

“…In particular, for this type of model, the total population size itself is perturbed directly by white noise. Examples of such models can be found in the works [15,16,10,[17][18][19] for instance. An sde model of an SEIR disease is studied in the paper [17] of Yang et al The papers [19] of Yuan et al and [18] of Yang and Mao study stability of sde multi-group SEIR models.…”

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: The Seir Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability of an SEIR epidemic model with independent stochastic perturbations

Witbooi

2013

Physica A: Statistical Mechanics and its Applications

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“…Hence equilibrium distributions obtained from the deterministic analysis are not realistic rather they fluctuate randomly around some average value. Lu [8] introduced stochasticity into the SIRS model (1) via the technique of parameter perturbation. He replaced the infection coefficient β by β + σ d B dt , where B is a Brownian motion defined on the complete probability space ( , F, {F t } t≥0 , P) with a filtration {F t } t≥0 satisfying the usual conditions and σ is the intensity of the noise.…”

Section: S(t) = μ − μS(t) − β S(t)i (T) + γ R(t) Dt D I (T) = [−(μ +mentioning

confidence: 99%

“…Lu [8] showed the local stability in probability of the disease-free equilibrium E 0 under the condition…”

Section: S(t) = μ − μS(t) − β S(t)i (T) + γ R(t) Dt D I (T) = [−(μ +mentioning

confidence: 99%

Dynamics of hybrid switching diffusions SIRS model

Settati¹,

Lahrouz²,

Jarroudi³

et al. 2015

J. Appl. Math. Comput.

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The main aim of this paper is to study the effect of the environmental noises in the asymptotic properties of a stochastic version of the classical SIRS epidemic model. The model studied here include white noise and telegraph noise modeled by Markovian switching. We obtained conditions for extinction both in probability one and in pth moment. We also established the persistence of disease under different conditions on the intensities of noises, the parameters of the model and the stationary distribution of the Markov chain. The highlight point of our work is that our conditions are sufficient and almost necessary for extinction and persistence of the epidemic. The presented results are demonstrated by numerical simulations.

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“…A stochastic version of the present model (with or without delay) has been considered in [13] for the stability of the disease free equilibrium. The stability of the disease-free of a SIRS model has been studied in [17].…”

Section: Introductionmentioning

confidence: 99%

Lyapunov exponent and almost sure asymptotic stability of a stochastic SIRS model

Chen

Liu

2014

Publicacions Matemàtiques

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Epidemiological models with bilinear incidence rate usually have an asymptotically stable trivial equilibrium corresponding to the disease-free state, or an asymptotically stable nontrivial equilibrium (i.e. interior equilibrium) corresponding to the endemic state. In this paper, we consider an epidemiological model, which is a SIRS (susceptible-infected-removed-susceptible) model influenced by random perturbations. We prove that the solutions of the system are positive for all positive initial conditions and that the solutions are global, that is, there is no finite explosion time. We present necessary and sufficient condition for the almost sure asymptotic stability of the steady state of the stochastic system. 2010 Mathematics Subject Classification: 92D30, 34D08, 34F05.

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Stability of SIRS system with random perturbations

Cited by 122 publications

References 9 publications

Stability of an SEIR epidemic model with independent stochastic perturbations

Stability of an SEIR epidemic model with independent stochastic perturbations

Dynamics of hybrid switching diffusions SIRS model

Lyapunov exponent and almost sure asymptotic stability of a stochastic SIRS model

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