Show simple item record

dc.contributor.authorWitbooi, Peter J.
dc.date.accessioned2017-05-22T10:47:20Z
dc.date.available2017-05-22T10:47:20Z
dc.date.issued2017
dc.identifier.citationWitbooi, P.J. (2017). An SEIRS epidemic model with stochastic transmission. Advances in Difference Equations, 2017: 109. http://dx.doi.org/10.1186/s13662-017-1166-6en_US
dc.identifier.issn1687-1847
dc.identifier.urihttp://hdl.handle.net/10566/2854
dc.identifier.urihttp://dx.doi.org/10.1186/s13662-017-1166-6
dc.description.abstractFor an SEIRS epidemic model with stochastic perturbations on transmission from the susceptible class to the latent and infectious classes, we prove the existence of global positive solutions. For sufficiently small values of the perturbation parameter, we prove the almost surely exponential stability of the disease-free equilibrium whenever a certain invariant R? is below unity. Here R?<R, the latter being the basic reproduction number of the underlying deterministic model. Biologically, the main result has the following significance for a disease model that has an incubation phase of the pathogen: A small stochastic perturbation on the transmission rate from susceptible to infectious via the latent phase will enhance the stability of the disease-free state if both components of the perturbation are non-trivial; otherwise the stability will not be disturbed. Simulations illustrate the main stability theorem.en_US
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.rightsCopyright, the Author. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).
dc.source.urihttp://dx.doi.org/10.1186/s13662-017-1166-6
dc.subjectOrdinary differential equations (ode)en_US
dc.subjectStochastic differential equation (sde)en_US
dc.titleAn SEIRS epidemic model with stochastic transmissionen_US
dc.typeArticleen_US
dc.privacy.showsubmitterFALSE
dc.status.ispeerreviewedTRUE
dc.description.accreditationISIen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record