Asymptotic properties of switching diffusion epidemic model with varying population size
The purpose of this work is to investigate the asymptotic properties of a stochastic version of the classical SIS epidemic model with standard incidence and varying population size. The stochastic model studied here includes white vector noise and telegraph noise modeled by Markovian switching. We e...
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| Veröffentlicht in: | Applied mathematics and computation 2013-08, Vol.219 (24), p.11134-11148 |
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| container_title | Applied mathematics and computation |
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| creator | Lahrouz, Aadil Settati, Adel |
| description | The purpose of this work is to investigate the asymptotic properties of a stochastic version of the classical SIS epidemic model with standard incidence and varying population size. The stochastic model studied here includes white vector noise and telegraph noise modeled by Markovian switching. We established 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 and the parameters of the model. Furthermore, we showed the existence of a stationary distribution and derive expressions for its mean and variance. The presented results are demonstrated by numerical simulations. |
| doi_str_mv | 10.1016/j.amc.2013.05.019 |
| format | Article |
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The stochastic model studied here includes white vector noise and telegraph noise modeled by Markovian switching. We established 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 and the parameters of the model. Furthermore, we showed the existence of a stationary distribution and derive expressions for its mean and variance. The presented results are demonstrated by numerical simulations.</description><identifier>ISSN: 0096-3003</identifier><identifier>EISSN: 1873-5649</identifier><identifier>DOI: 10.1016/j.amc.2013.05.019</identifier><language>eng</language><publisher>Elsevier Inc</publisher><subject>Extinction ; Markovian switching ; Stationary distribution ; Stochastic epidemic model ; Stochastic persistence</subject><ispartof>Applied mathematics and computation, 2013-08, Vol.219 (24), p.11134-11148</ispartof><rights>2013 Elsevier Inc.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c330t-cfffa7e116b76ed1e1e5a59cbb0720b769c5b2096272eb0373b899e1682869283</citedby><cites>FETCH-LOGICAL-c330t-cfffa7e116b76ed1e1e5a59cbb0720b769c5b2096272eb0373b899e1682869283</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.amc.2013.05.019$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,777,781,3537,27905,27906,45976</link.rule.ids></links><search><creatorcontrib>Lahrouz, Aadil</creatorcontrib><creatorcontrib>Settati, Adel</creatorcontrib><title>Asymptotic properties of switching diffusion epidemic model with varying population size</title><title>Applied mathematics and computation</title><description>The purpose of this work is to investigate the asymptotic properties of a stochastic version of the classical SIS epidemic model with standard incidence and varying population size. 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The presented results are demonstrated by numerical simulations.</description><subject>Extinction</subject><subject>Markovian switching</subject><subject>Stationary distribution</subject><subject>Stochastic epidemic model</subject><subject>Stochastic persistence</subject><issn>0096-3003</issn><issn>1873-5649</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMouK7-AG89emmdNG3a4GlZ_IIFLwreQptO3Cztpibpiv56U9azp4HheYd3HkKuKWQUKL_dZc2gshwoy6DMgIoTsqB1xdKSF-KULAAETxkAOycX3u8AoOK0WJD3lf8exmCDUcno7IguGPSJ1Yn_MkFtzf4j6YzWkzd2n-BoOhwiOtgO-yQS2-TQuO-ZGu049U2YMW9-8JKc6ab3ePU3l-Tt4f51_ZRuXh6f16tNqhiDkCqtdVMhpbytOHYUKZZNKVTbQpVD3AlVtnksn1c5tsAq1tZCIOV1XnOR12xJbo53Y_vPCX2Qg_EK-77Zo528pOX8asGKIqL0iCpnvXeo5ejMEOtLCnK2KHcyWpSzRQmljBZj5u6YwfjDwaCTXhncK-yMQxVkZ80_6V-G1nuq</recordid><startdate>20130815</startdate><enddate>20130815</enddate><creator>Lahrouz, Aadil</creator><creator>Settati, Adel</creator><general>Elsevier Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7T2</scope><scope>7U2</scope><scope>C1K</scope></search><sort><creationdate>20130815</creationdate><title>Asymptotic properties of switching diffusion epidemic model with varying population size</title><author>Lahrouz, Aadil ; Settati, Adel</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c330t-cfffa7e116b76ed1e1e5a59cbb0720b769c5b2096272eb0373b899e1682869283</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Extinction</topic><topic>Markovian switching</topic><topic>Stationary distribution</topic><topic>Stochastic epidemic model</topic><topic>Stochastic persistence</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lahrouz, Aadil</creatorcontrib><creatorcontrib>Settati, Adel</creatorcontrib><collection>CrossRef</collection><collection>Health and Safety Science Abstracts (Full archive)</collection><collection>Safety Science and Risk</collection><collection>Environmental Sciences and Pollution Management</collection><jtitle>Applied mathematics and computation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lahrouz, Aadil</au><au>Settati, Adel</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Asymptotic properties of switching diffusion epidemic model with varying population size</atitle><jtitle>Applied mathematics and computation</jtitle><date>2013-08-15</date><risdate>2013</risdate><volume>219</volume><issue>24</issue><spage>11134</spage><epage>11148</epage><pages>11134-11148</pages><issn>0096-3003</issn><eissn>1873-5649</eissn><abstract>The purpose of this work is to investigate the asymptotic properties of a stochastic version of the classical SIS epidemic model with standard incidence and varying population size. 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| ispartof | Applied mathematics and computation, 2013-08, Vol.219 (24), p.11134-11148 |
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| source | Elsevier ScienceDirect Journals |
| subjects | Extinction Markovian switching Stationary distribution Stochastic epidemic model Stochastic persistence |
| title | Asymptotic properties of switching diffusion epidemic model with varying population size |
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