Analysis of Malaria Control Measures’ Effectiveness Using Multistage Vector Model
We analyze an epidemiological model to evaluate the effectiveness of multiple means of control in malaria-endemic areas. The mathematical model consists of a system of several ordinary differential equations and is based on a multi-compartment representation of the system. The model takes into accou...
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| Veröffentlicht in: | Bulletin of mathematical biology 2019-11, Vol.81 (11), p.4366-4411 |
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| creator | Kamgang, Jean Claude Thron, Christopher Penniman |
| description | We analyze an epidemiological model to evaluate the effectiveness of multiple means of control in malaria-endemic areas. The mathematical model consists of a system of several ordinary differential equations and is based on a multi-compartment representation of the system. The model takes into account the multiple resting–questing stages undergone by adult female mosquitoes during the period in which they function as disease vectors. We compute the basic reproduction number
R
0
and show that if
R
0
≤
1
, the disease-free equilibrium is globally asymptotically stable (GAS) on the nonnegative orthant. If
R
0
>
1
, the system admits a unique endemic equilibrium (EE) that is GAS. We perform a sensitivity analysis of the dependence of
R
0
and the EE on parameters related to control measures, such as killing effectiveness and bite prevention. Finally, we discuss the implications for a comprehensive, cost-effective strategy for malaria control. |
| doi_str_mv | 10.1007/s11538-019-00637-6 |
| format | Article |
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R
0
and show that if
R
0
≤
1
, the disease-free equilibrium is globally asymptotically stable (GAS) on the nonnegative orthant. If
R
0
>
1
, the system admits a unique endemic equilibrium (EE) that is GAS. We perform a sensitivity analysis of the dependence of
R
0
and the EE on parameters related to control measures, such as killing effectiveness and bite prevention. Finally, we discuss the implications for a comprehensive, cost-effective strategy for malaria control.</description><identifier>ISSN: 0092-8240</identifier><identifier>EISSN: 1522-9602</identifier><identifier>DOI: 10.1007/s11538-019-00637-6</identifier><identifier>PMID: 31286347</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Cell Biology ; Dependence ; Differential equations ; Epidemiology ; Life Sciences ; Malaria ; Mathematical and Computational Biology ; Mathematical models ; Mathematics ; Mathematics and Statistics ; Ordinary differential equations ; Sensitivity analysis ; Special Issue: Mathematical Epidemiology ; Vector-borne diseases ; Vectors</subject><ispartof>Bulletin of mathematical biology, 2019-11, Vol.81 (11), p.4366-4411</ispartof><rights>Society for Mathematical Biology 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c375t-92633cf03e54b8c9e1931bf2504bb59a70387caf0a932fc3f86a431e173474603</citedby><cites>FETCH-LOGICAL-c375t-92633cf03e54b8c9e1931bf2504bb59a70387caf0a932fc3f86a431e173474603</cites><orcidid>0000-0002-3903-2283 ; 0000-0002-8960-2504</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/s11538-019-00637-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11538-019-00637-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/31286347$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Kamgang, Jean Claude</creatorcontrib><creatorcontrib>Thron, Christopher Penniman</creatorcontrib><title>Analysis of Malaria Control Measures’ Effectiveness Using Multistage Vector Model</title><title>Bulletin of mathematical biology</title><addtitle>Bull Math Biol</addtitle><addtitle>Bull Math Biol</addtitle><description>We analyze an epidemiological model to evaluate the effectiveness of multiple means of control in malaria-endemic areas. The mathematical model consists of a system of several ordinary differential equations and is based on a multi-compartment representation of the system. The model takes into account the multiple resting–questing stages undergone by adult female mosquitoes during the period in which they function as disease vectors. We compute the basic reproduction number
R
0
and show that if
R
0
≤
1
, the disease-free equilibrium is globally asymptotically stable (GAS) on the nonnegative orthant. If
R
0
>
1
, the system admits a unique endemic equilibrium (EE) that is GAS. We perform a sensitivity analysis of the dependence of
R
0
and the EE on parameters related to control measures, such as killing effectiveness and bite prevention. Finally, we discuss the implications for a comprehensive, cost-effective strategy for malaria control.</description><subject>Cell Biology</subject><subject>Dependence</subject><subject>Differential equations</subject><subject>Epidemiology</subject><subject>Life Sciences</subject><subject>Malaria</subject><subject>Mathematical and Computational Biology</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Ordinary differential equations</subject><subject>Sensitivity analysis</subject><subject>Special Issue: Mathematical Epidemiology</subject><subject>Vector-borne diseases</subject><subject>Vectors</subject><issn>0092-8240</issn><issn>1522-9602</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9kMFO3DAQhi3UCrYLL9BDZamXXlLGnjiJj2hFCxIrDi1cLSeMV0HZmHqSStz6Grxen6SmS0HqAfngw3z_7_EnxHsFnxVAfcxKGWwKULYAqLAuqj2xUEbrwlag34gFgNVFo0s4EO-YbyGHLNp9cYBKNxWW9UJ8Oxn9cM89yxjk2g8-9V6u4jilOMg1eZ4T8e9fD_I0BOqm_ieNxCyvuB83cj0PU8-T35C8zsOY5Dre0HAo3gY_MB093Utx9eX0--qsuLj8er46uSg6rM1UWF0hdgGQTNk2nSVlUbVBGyjb1lhfAzZ15wN4izp0GJrKl6hI1XnzsgJcik-73rsUf8zEk9v23NEw-JHizE5rUxrVNMZk9ON_6G2cU_56plDV2Z7KZyn0jupSZE4U3F3qtz7dOwXuUbnbKXdZufur3FU59OGpem63dPMc-ec4A7gDOI_GDaWXt1-p_QNgb4tV</recordid><startdate>20191101</startdate><enddate>20191101</enddate><creator>Kamgang, Jean Claude</creator><creator>Thron, Christopher Penniman</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SS</scope><scope>7TK</scope><scope>JQ2</scope><scope>K9.</scope><scope>7X8</scope><orcidid>https://orcid.org/0000-0002-3903-2283</orcidid><orcidid>https://orcid.org/0000-0002-8960-2504</orcidid></search><sort><creationdate>20191101</creationdate><title>Analysis of Malaria Control Measures’ Effectiveness Using Multistage Vector Model</title><author>Kamgang, Jean Claude ; Thron, Christopher Penniman</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c375t-92633cf03e54b8c9e1931bf2504bb59a70387caf0a932fc3f86a431e173474603</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Cell Biology</topic><topic>Dependence</topic><topic>Differential equations</topic><topic>Epidemiology</topic><topic>Life Sciences</topic><topic>Malaria</topic><topic>Mathematical and Computational Biology</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Ordinary differential equations</topic><topic>Sensitivity analysis</topic><topic>Special Issue: Mathematical Epidemiology</topic><topic>Vector-borne diseases</topic><topic>Vectors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kamgang, Jean Claude</creatorcontrib><creatorcontrib>Thron, Christopher Penniman</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>Entomology Abstracts (Full archive)</collection><collection>Neurosciences Abstracts</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><collection>MEDLINE - Academic</collection><jtitle>Bulletin of mathematical biology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kamgang, Jean Claude</au><au>Thron, Christopher Penniman</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Analysis of Malaria Control Measures’ Effectiveness Using Multistage Vector Model</atitle><jtitle>Bulletin of mathematical biology</jtitle><stitle>Bull Math Biol</stitle><addtitle>Bull Math Biol</addtitle><date>2019-11-01</date><risdate>2019</risdate><volume>81</volume><issue>11</issue><spage>4366</spage><epage>4411</epage><pages>4366-4411</pages><issn>0092-8240</issn><eissn>1522-9602</eissn><abstract>We analyze an epidemiological model to evaluate the effectiveness of multiple means of control in malaria-endemic areas. The mathematical model consists of a system of several ordinary differential equations and is based on a multi-compartment representation of the system. The model takes into account the multiple resting–questing stages undergone by adult female mosquitoes during the period in which they function as disease vectors. We compute the basic reproduction number
R
0
and show that if
R
0
≤
1
, the disease-free equilibrium is globally asymptotically stable (GAS) on the nonnegative orthant. If
R
0
>
1
, the system admits a unique endemic equilibrium (EE) that is GAS. We perform a sensitivity analysis of the dependence of
R
0
and the EE on parameters related to control measures, such as killing effectiveness and bite prevention. Finally, we discuss the implications for a comprehensive, cost-effective strategy for malaria control.</abstract><cop>New York</cop><pub>Springer US</pub><pmid>31286347</pmid><doi>10.1007/s11538-019-00637-6</doi><tpages>46</tpages><orcidid>https://orcid.org/0000-0002-3903-2283</orcidid><orcidid>https://orcid.org/0000-0002-8960-2504</orcidid></addata></record> |
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| subjects | Cell Biology Dependence Differential equations Epidemiology Life Sciences Malaria Mathematical and Computational Biology Mathematical models Mathematics Mathematics and Statistics Ordinary differential equations Sensitivity analysis Special Issue: Mathematical Epidemiology Vector-borne diseases Vectors |
| title | Analysis of Malaria Control Measures’ Effectiveness Using Multistage Vector Model |
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