2009
DOI: 10.1016/j.physa.2009.05.036
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Stability of SIRS system with random perturbations

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Cited by 122 publications
(58 citation statements)
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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%
See 1 more Smart Citation
“…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%
“…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%
“…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%