Resistance to antibiotics: limit theorems for a stochastic SIS model structured by level of resistance
The rise of bacterial resistance to antibiotics is a major Public Health concern. It is the result of two interacting processes: the selection of resistant bacterial strains under exposure to antibiotics and the dissemination of bacterial strains throughout the population by contact between colonize...
Gespeichert in:
| Veröffentlicht in: | Journal of mathematical biology 2016-12, Vol.73 (6-7), p.1353-1378 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1378 |
|---|---|
| container_issue | 6-7 |
| container_start_page | 1353 |
| container_title | Journal of mathematical biology |
| container_volume | 73 |
| creator | Boëlle, Pierre-Yves Thomas, Guy |
| description | The rise of bacterial resistance to antibiotics is a major Public Health concern. It is the result of two interacting processes: the selection of resistant bacterial strains under exposure to antibiotics and the dissemination of bacterial strains throughout the population by contact between colonized and uncolonized individuals. To investigate the resulting time evolution of bacterial resistance, Temime et al. (Emerg Infect Dis 9:411–417,
2003
) developed a stochastic SIS model, which was structured by the level of resistance of bacterial strains. Here we study the asymptotic properties of this model when the population size is large. To this end, we cast the model within the framework of measure valued processes, using point measures to represent the pattern of bacterial resistance in the compartments of colonized individuals. We first show that the suitably normalized model tends in probability to the solution of a deterministic differential system. Then we prove that the process of fluctuations around this limit tends in law to a Gaussian process in a space of distributions. These results, which generalize those of Kurtz (CBMS-NSF regional conference series in applied mathematics, vol 36. Society for Industrial and Applied Mathematics (SIAM), Philadelphia,
1981
, chap. 8) on SIR models, support the validity of the deterministic approximation and quantify the rate of convergence. |
| doi_str_mv | 10.1007/s00285-016-0996-2 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_hal_p</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_01303276v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1846405428</sourcerecordid><originalsourceid>FETCH-LOGICAL-c482t-fcfab13498984844b59a7ffa787fe364926cfb134075943b601eb105a43ad2523</originalsourceid><addsrcrecordid>eNqNkU1rFTEYhYMo9rb6A9xIwI1djL75nIy7UuwHXCi0ug6Z3MSbMjOpSabQf2-GqRcRBFeBkycn73kPQu8IfCIA7ecMQJVogMgGuk429AXaEM5oQziRL9EGGLBGKkKP0HHO9wCkFR15jY5oC4xKTjbI37occjGTdbhEbKYS-hBLsPkLHsIYCi57F5MbM_YxYYNziXZvciXw3fUdHuPODVVMsy1zcjvcP-HBPVYtepwO3m_QK2-G7N4-nyfo-8XXb-dXzfbm8vr8bNtYrmhpvPWmJ4x3qlNccd6LzrTem1a13jHJOyqtXwCoQTjrJRDXExCGM7OjgrITdLr67s2gH1IYTXrS0QR9dbbViwak7oS28pFU9uPKPqT4c3a56DFk64bBTC7OWRPFJQfBqfoPlEoplWC8oh_-Qu_jnKYaeqFqF0IwVimyUjbFnJPzh2EJ6KVbvXZb55V66VYv2d4_O8_96HaHF7_LrABdgVyvph8u_fH1P11_AaIjrKA</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1828125533</pqid></control><display><type>article</type><title>Resistance to antibiotics: limit theorems for a stochastic SIS model structured by level of resistance</title><source>MEDLINE</source><source>SpringerLink Journals - AutoHoldings</source><creator>Boëlle, Pierre-Yves ; Thomas, Guy</creator><creatorcontrib>Boëlle, Pierre-Yves ; Thomas, Guy</creatorcontrib><description>The rise of bacterial resistance to antibiotics is a major Public Health concern. It is the result of two interacting processes: the selection of resistant bacterial strains under exposure to antibiotics and the dissemination of bacterial strains throughout the population by contact between colonized and uncolonized individuals. To investigate the resulting time evolution of bacterial resistance, Temime et al. (Emerg Infect Dis 9:411–417,
2003
) developed a stochastic SIS model, which was structured by the level of resistance of bacterial strains. Here we study the asymptotic properties of this model when the population size is large. To this end, we cast the model within the framework of measure valued processes, using point measures to represent the pattern of bacterial resistance in the compartments of colonized individuals. We first show that the suitably normalized model tends in probability to the solution of a deterministic differential system. Then we prove that the process of fluctuations around this limit tends in law to a Gaussian process in a space of distributions. These results, which generalize those of Kurtz (CBMS-NSF regional conference series in applied mathematics, vol 36. Society for Industrial and Applied Mathematics (SIAM), Philadelphia,
1981
, chap. 8) on SIR models, support the validity of the deterministic approximation and quantify the rate of convergence.</description><identifier>ISSN: 0303-6812</identifier><identifier>EISSN: 1432-1416</identifier><identifier>DOI: 10.1007/s00285-016-0996-2</identifier><identifier>PMID: 27032641</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Anti-Bacterial Agents - pharmacology ; Applications of Mathematics ; Bacteria - drug effects ; Biological Evolution ; Drug Resistance, Microbial ; Humans ; Life Sciences ; Mathematical and Computational Biology ; Mathematics ; Mathematics and Statistics ; Models, Statistical ; Population Density ; Probability ; Santé publique et épidémiologie ; Stochastic Processes ; Time Factors</subject><ispartof>Journal of mathematical biology, 2016-12, Vol.73 (6-7), p.1353-1378</ispartof><rights>Springer-Verlag Berlin Heidelberg 2016</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c482t-fcfab13498984844b59a7ffa787fe364926cfb134075943b601eb105a43ad2523</citedby><cites>FETCH-LOGICAL-c482t-fcfab13498984844b59a7ffa787fe364926cfb134075943b601eb105a43ad2523</cites><orcidid>0000-0002-5367-8232</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00285-016-0996-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00285-016-0996-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,314,780,784,885,27924,27925,41488,42557,51319</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/27032641$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink><backlink>$$Uhttps://hal.sorbonne-universite.fr/hal-01303276$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Boëlle, Pierre-Yves</creatorcontrib><creatorcontrib>Thomas, Guy</creatorcontrib><title>Resistance to antibiotics: limit theorems for a stochastic SIS model structured by level of resistance</title><title>Journal of mathematical biology</title><addtitle>J. Math. Biol</addtitle><addtitle>J Math Biol</addtitle><description>The rise of bacterial resistance to antibiotics is a major Public Health concern. It is the result of two interacting processes: the selection of resistant bacterial strains under exposure to antibiotics and the dissemination of bacterial strains throughout the population by contact between colonized and uncolonized individuals. To investigate the resulting time evolution of bacterial resistance, Temime et al. (Emerg Infect Dis 9:411–417,
2003
) developed a stochastic SIS model, which was structured by the level of resistance of bacterial strains. Here we study the asymptotic properties of this model when the population size is large. To this end, we cast the model within the framework of measure valued processes, using point measures to represent the pattern of bacterial resistance in the compartments of colonized individuals. We first show that the suitably normalized model tends in probability to the solution of a deterministic differential system. Then we prove that the process of fluctuations around this limit tends in law to a Gaussian process in a space of distributions. These results, which generalize those of Kurtz (CBMS-NSF regional conference series in applied mathematics, vol 36. Society for Industrial and Applied Mathematics (SIAM), Philadelphia,
1981
, chap. 8) on SIR models, support the validity of the deterministic approximation and quantify the rate of convergence.</description><subject>Anti-Bacterial Agents - pharmacology</subject><subject>Applications of Mathematics</subject><subject>Bacteria - drug effects</subject><subject>Biological Evolution</subject><subject>Drug Resistance, Microbial</subject><subject>Humans</subject><subject>Life Sciences</subject><subject>Mathematical and Computational Biology</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Models, Statistical</subject><subject>Population Density</subject><subject>Probability</subject><subject>Santé publique et épidémiologie</subject><subject>Stochastic Processes</subject><subject>Time Factors</subject><issn>0303-6812</issn><issn>1432-1416</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNqNkU1rFTEYhYMo9rb6A9xIwI1djL75nIy7UuwHXCi0ug6Z3MSbMjOpSabQf2-GqRcRBFeBkycn73kPQu8IfCIA7ecMQJVogMgGuk429AXaEM5oQziRL9EGGLBGKkKP0HHO9wCkFR15jY5oC4xKTjbI37occjGTdbhEbKYS-hBLsPkLHsIYCi57F5MbM_YxYYNziXZvciXw3fUdHuPODVVMsy1zcjvcP-HBPVYtepwO3m_QK2-G7N4-nyfo-8XXb-dXzfbm8vr8bNtYrmhpvPWmJ4x3qlNccd6LzrTem1a13jHJOyqtXwCoQTjrJRDXExCGM7OjgrITdLr67s2gH1IYTXrS0QR9dbbViwak7oS28pFU9uPKPqT4c3a56DFk64bBTC7OWRPFJQfBqfoPlEoplWC8oh_-Qu_jnKYaeqFqF0IwVimyUjbFnJPzh2EJ6KVbvXZb55V66VYv2d4_O8_96HaHF7_LrABdgVyvph8u_fH1P11_AaIjrKA</recordid><startdate>20161201</startdate><enddate>20161201</enddate><creator>Boëlle, Pierre-Yves</creator><creator>Thomas, Guy</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><general>Springer</general><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7TK</scope><scope>7TM</scope><scope>7U9</scope><scope>7X7</scope><scope>7XB</scope><scope>88A</scope><scope>88E</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FH</scope><scope>8FI</scope><scope>8FJ</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BBNVY</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FYUFA</scope><scope>GHDGH</scope><scope>GNUQQ</scope><scope>H94</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>K9.</scope><scope>L6V</scope><scope>LK8</scope><scope>M0S</scope><scope>M1P</scope><scope>M7N</scope><scope>M7P</scope><scope>M7S</scope><scope>M7Z</scope><scope>P5Z</scope><scope>P62</scope><scope>P64</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>7X8</scope><scope>7QL</scope><scope>C1K</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0002-5367-8232</orcidid></search><sort><creationdate>20161201</creationdate><title>Resistance to antibiotics: limit theorems for a stochastic SIS model structured by level of resistance</title><author>Boëlle, Pierre-Yves ; Thomas, Guy</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c482t-fcfab13498984844b59a7ffa787fe364926cfb134075943b601eb105a43ad2523</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Anti-Bacterial Agents - pharmacology</topic><topic>Applications of Mathematics</topic><topic>Bacteria - drug effects</topic><topic>Biological Evolution</topic><topic>Drug Resistance, Microbial</topic><topic>Humans</topic><topic>Life Sciences</topic><topic>Mathematical and Computational Biology</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Models, Statistical</topic><topic>Population Density</topic><topic>Probability</topic><topic>Santé publique et épidémiologie</topic><topic>Stochastic Processes</topic><topic>Time Factors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Boëlle, Pierre-Yves</creatorcontrib><creatorcontrib>Thomas, Guy</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Neurosciences Abstracts</collection><collection>Nucleic Acids Abstracts</collection><collection>Virology and AIDS Abstracts</collection><collection>Health & Medical Collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Biology Database (Alumni Edition)</collection><collection>Medical Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>Hospital Premium Collection</collection><collection>Hospital Premium Collection (Alumni Edition)</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>Biological Science Collection</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>Health Research Premium Collection</collection><collection>Health Research Premium Collection (Alumni)</collection><collection>ProQuest Central Student</collection><collection>AIDS and Cancer Research Abstracts</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Biological Science Collection</collection><collection>Health & Medical Collection (Alumni Edition)</collection><collection>Medical Database</collection><collection>Algology Mycology and Protozoology Abstracts (Microbiology C)</collection><collection>Biological Science Database</collection><collection>Engineering Database</collection><collection>Biochemistry Abstracts 1</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Biotechnology and BioEngineering Abstracts</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>MEDLINE - Academic</collection><collection>Bacteriology Abstracts (Microbiology B)</collection><collection>Environmental Sciences and Pollution Management</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Journal of mathematical biology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Boëlle, Pierre-Yves</au><au>Thomas, Guy</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Resistance to antibiotics: limit theorems for a stochastic SIS model structured by level of resistance</atitle><jtitle>Journal of mathematical biology</jtitle><stitle>J. Math. Biol</stitle><addtitle>J Math Biol</addtitle><date>2016-12-01</date><risdate>2016</risdate><volume>73</volume><issue>6-7</issue><spage>1353</spage><epage>1378</epage><pages>1353-1378</pages><issn>0303-6812</issn><eissn>1432-1416</eissn><abstract>The rise of bacterial resistance to antibiotics is a major Public Health concern. It is the result of two interacting processes: the selection of resistant bacterial strains under exposure to antibiotics and the dissemination of bacterial strains throughout the population by contact between colonized and uncolonized individuals. To investigate the resulting time evolution of bacterial resistance, Temime et al. (Emerg Infect Dis 9:411–417,
2003
) developed a stochastic SIS model, which was structured by the level of resistance of bacterial strains. Here we study the asymptotic properties of this model when the population size is large. To this end, we cast the model within the framework of measure valued processes, using point measures to represent the pattern of bacterial resistance in the compartments of colonized individuals. We first show that the suitably normalized model tends in probability to the solution of a deterministic differential system. Then we prove that the process of fluctuations around this limit tends in law to a Gaussian process in a space of distributions. These results, which generalize those of Kurtz (CBMS-NSF regional conference series in applied mathematics, vol 36. Society for Industrial and Applied Mathematics (SIAM), Philadelphia,
1981
, chap. 8) on SIR models, support the validity of the deterministic approximation and quantify the rate of convergence.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><pmid>27032641</pmid><doi>10.1007/s00285-016-0996-2</doi><tpages>26</tpages><orcidid>https://orcid.org/0000-0002-5367-8232</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0303-6812 |
| ispartof | Journal of mathematical biology, 2016-12, Vol.73 (6-7), p.1353-1378 |
| issn | 0303-6812 1432-1416 |
| language | eng |
| recordid | cdi_hal_primary_oai_HAL_hal_01303276v1 |
| source | MEDLINE; SpringerLink Journals - AutoHoldings |
| subjects | Anti-Bacterial Agents - pharmacology Applications of Mathematics Bacteria - drug effects Biological Evolution Drug Resistance, Microbial Humans Life Sciences Mathematical and Computational Biology Mathematics Mathematics and Statistics Models, Statistical Population Density Probability Santé publique et épidémiologie Stochastic Processes Time Factors |
| title | Resistance to antibiotics: limit theorems for a stochastic SIS model structured by level of resistance |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-05T07%3A39%3A55IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_hal_p&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Resistance%20to%20antibiotics:%20limit%20theorems%20for%20a%20stochastic%20SIS%20model%20structured%20by%20level%20of%20resistance&rft.jtitle=Journal%20of%20mathematical%20biology&rft.au=Bo%C3%ABlle,%20Pierre-Yves&rft.date=2016-12-01&rft.volume=73&rft.issue=6-7&rft.spage=1353&rft.epage=1378&rft.pages=1353-1378&rft.issn=0303-6812&rft.eissn=1432-1416&rft_id=info:doi/10.1007/s00285-016-0996-2&rft_dat=%3Cproquest_hal_p%3E1846405428%3C/proquest_hal_p%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1828125533&rft_id=info:pmid/27032641&rfr_iscdi=true |