Stability of an SEIR epidemic model with indepenent stochastic perturbations
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Date
2013
Authors
Journal Title
Journal ISSN
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Publisher
Elsevier
Abstract
For 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, Rσ , of the basic reproduction number R0 of the deterministic special case.
Whenever σ > 0 then Rσ < R0. For small values of σ, the stability theorem guarantees
almost sure exponential stability whenever Rσ < 1. We also discuss the effect of increasing
σ.
Description
Keywords
SEIR, epidemic, model, stochastic perturbations
Citation
Witbooi, P. J. (2013). Stability of an SEIR epidemic model with independent stochastic perturbations. Physica A, 392(20): 4928–4936