Optimal Control of Aquatic Diseases: A Case Study of Yemen’s Cholera Outbreak
We propose a mathematical model for the transmission dynamics of some strains of the bacterium Vibrio cholerae , responsible for the cholera disease in humans. We prove that, when the basic reproduction number is equal to one, a transcritical bifurcation occurs for which the endemic equilibrium eman...
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| Veröffentlicht in: | Journal of optimization theory and applications 2020-06, Vol.185 (3), p.1008-1030 |
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| creator | Lemos-Paião, Ana P. Silva, Cristiana J. Torres, Delfim F. M. Venturino, Ezio |
| description | We propose a mathematical model for the transmission dynamics of some strains of the bacterium
Vibrio cholerae
, responsible for the cholera disease in humans. We prove that, when the basic reproduction number is equal to one, a transcritical bifurcation occurs for which the endemic equilibrium emanates from the disease-free point. A control function is introduced into the model, representing the distribution of chlorine water tablets for water purification. An optimal control problem is then proposed and analyzed, where the goal is to determine the fraction of susceptible individuals who should have access to chlorine water tablets in order to minimize the total number of new infections plus the total cost associated with the distribution of chlorine water tablets, over the considered period of time. Finally, we consider real data of the cholera outbreak in Yemen, from April 27, 2017 to April 15, 2018, choosing the values of the parameters of the uncontrolled model that fit the real data. Using our optimal control results, we show, numerically, that the distribution of chlorine water tablets could have stopped, in a fast way, the worst cholera outbreak that ever occurred in human history. Due to the critical situation of Yemen, we also simulate the case where only a small percentage of susceptible individuals has access to chlorine water tablets and obtain an optimal control solution that decreases, substantially, the maximum number of infective individuals affected by the outbreak. |
| doi_str_mv | 10.1007/s10957-020-01668-z |
| format | Article |
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Vibrio cholerae
, responsible for the cholera disease in humans. We prove that, when the basic reproduction number is equal to one, a transcritical bifurcation occurs for which the endemic equilibrium emanates from the disease-free point. A control function is introduced into the model, representing the distribution of chlorine water tablets for water purification. An optimal control problem is then proposed and analyzed, where the goal is to determine the fraction of susceptible individuals who should have access to chlorine water tablets in order to minimize the total number of new infections plus the total cost associated with the distribution of chlorine water tablets, over the considered period of time. Finally, we consider real data of the cholera outbreak in Yemen, from April 27, 2017 to April 15, 2018, choosing the values of the parameters of the uncontrolled model that fit the real data. Using our optimal control results, we show, numerically, that the distribution of chlorine water tablets could have stopped, in a fast way, the worst cholera outbreak that ever occurred in human history. Due to the critical situation of Yemen, we also simulate the case where only a small percentage of susceptible individuals has access to chlorine water tablets and obtain an optimal control solution that decreases, substantially, the maximum number of infective individuals affected by the outbreak.</description><identifier>ISSN: 0022-3239</identifier><identifier>EISSN: 1573-2878</identifier><identifier>DOI: 10.1007/s10957-020-01668-z</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Applications of Mathematics ; Bifurcations ; Calculus of Variations and Optimal Control; Optimization ; Chlorine ; Cholera ; Computer simulation ; Disease control ; Engineering ; Mathematical models ; Mathematics ; Mathematics and Statistics ; Operations Research/Decision Theory ; Optimal control ; Optimization ; Outbreaks ; Tablets ; Theory of Computation ; Water purification</subject><ispartof>Journal of optimization theory and applications, 2020-06, Vol.185 (3), p.1008-1030</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020</rights><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c384t-113592a25a3fc9e36c835b140637c2a3b871d1e906e43fb4b0efa68b98579f553</citedby><cites>FETCH-LOGICAL-c384t-113592a25a3fc9e36c835b140637c2a3b871d1e906e43fb4b0efa68b98579f553</cites><orcidid>0000-0001-7215-5114 ; 0000-0001-8641-2505 ; 0000-0002-7238-546X ; 0000-0003-4592-3426</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/s10957-020-01668-z$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10957-020-01668-z$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Lemos-Paião, Ana P.</creatorcontrib><creatorcontrib>Silva, Cristiana J.</creatorcontrib><creatorcontrib>Torres, Delfim F. M.</creatorcontrib><creatorcontrib>Venturino, Ezio</creatorcontrib><title>Optimal Control of Aquatic Diseases: A Case Study of Yemen’s Cholera Outbreak</title><title>Journal of optimization theory and applications</title><addtitle>J Optim Theory Appl</addtitle><description>We propose a mathematical model for the transmission dynamics of some strains of the bacterium
Vibrio cholerae
, responsible for the cholera disease in humans. We prove that, when the basic reproduction number is equal to one, a transcritical bifurcation occurs for which the endemic equilibrium emanates from the disease-free point. A control function is introduced into the model, representing the distribution of chlorine water tablets for water purification. An optimal control problem is then proposed and analyzed, where the goal is to determine the fraction of susceptible individuals who should have access to chlorine water tablets in order to minimize the total number of new infections plus the total cost associated with the distribution of chlorine water tablets, over the considered period of time. Finally, we consider real data of the cholera outbreak in Yemen, from April 27, 2017 to April 15, 2018, choosing the values of the parameters of the uncontrolled model that fit the real data. Using our optimal control results, we show, numerically, that the distribution of chlorine water tablets could have stopped, in a fast way, the worst cholera outbreak that ever occurred in human history. Due to the critical situation of Yemen, we also simulate the case where only a small percentage of susceptible individuals has access to chlorine water tablets and obtain an optimal control solution that decreases, substantially, the maximum number of infective individuals affected by the outbreak.</description><subject>Applications of Mathematics</subject><subject>Bifurcations</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Chlorine</subject><subject>Cholera</subject><subject>Computer simulation</subject><subject>Disease control</subject><subject>Engineering</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operations Research/Decision Theory</subject><subject>Optimal control</subject><subject>Optimization</subject><subject>Outbreaks</subject><subject>Tablets</subject><subject>Theory of Computation</subject><subject>Water purification</subject><issn>0022-3239</issn><issn>1573-2878</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp9kLFOwzAQhi0EEqXwAkyWmA1nO45ttipQQKqUARiYLCd1oCVNWjsZ2onX4PV4ElyCxIZ00t3w_Xe6D6FzCpcUQF4FClpIAgwI0DRVZHeARlRITpiS6hCNABgjnHF9jE5CWAKAVjIZoTxfd4uVrXHWNp1va9xWeLLpbbco8c0iOBtcuMYTnMUBP3b9fLsnXtzKNV8fnwFnb23tvMV53xXe2fdTdFTZOriz3z5Gz9Pbp-yezPK7h2wyIyVXSUco5UIzy4TlVakdT0vFRUETSLksmeWFknROnYbUJbwqkgJcZVNVaCWkroTgY3Qx7F37dtO70Jll2_smnjQsobE0lzRSbKBK34bgXWXWPn7rt4aC2YszgzgTxZkfcWYXQ3wIhQg3r87_rf4n9Q0T-HB1</recordid><startdate>20200601</startdate><enddate>20200601</enddate><creator>Lemos-Paião, Ana P.</creator><creator>Silva, Cristiana J.</creator><creator>Torres, Delfim F. 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M. ; Venturino, Ezio</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c384t-113592a25a3fc9e36c835b140637c2a3b871d1e906e43fb4b0efa68b98579f553</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Applications of Mathematics</topic><topic>Bifurcations</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Chlorine</topic><topic>Cholera</topic><topic>Computer simulation</topic><topic>Disease control</topic><topic>Engineering</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operations Research/Decision Theory</topic><topic>Optimal control</topic><topic>Optimization</topic><topic>Outbreaks</topic><topic>Tablets</topic><topic>Theory of Computation</topic><topic>Water purification</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lemos-Paião, Ana P.</creatorcontrib><creatorcontrib>Silva, Cristiana J.</creatorcontrib><creatorcontrib>Torres, Delfim F. 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M.</au><au>Venturino, Ezio</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimal Control of Aquatic Diseases: A Case Study of Yemen’s Cholera Outbreak</atitle><jtitle>Journal of optimization theory and applications</jtitle><stitle>J Optim Theory Appl</stitle><date>2020-06-01</date><risdate>2020</risdate><volume>185</volume><issue>3</issue><spage>1008</spage><epage>1030</epage><pages>1008-1030</pages><issn>0022-3239</issn><eissn>1573-2878</eissn><abstract>We propose a mathematical model for the transmission dynamics of some strains of the bacterium
Vibrio cholerae
, responsible for the cholera disease in humans. We prove that, when the basic reproduction number is equal to one, a transcritical bifurcation occurs for which the endemic equilibrium emanates from the disease-free point. A control function is introduced into the model, representing the distribution of chlorine water tablets for water purification. An optimal control problem is then proposed and analyzed, where the goal is to determine the fraction of susceptible individuals who should have access to chlorine water tablets in order to minimize the total number of new infections plus the total cost associated with the distribution of chlorine water tablets, over the considered period of time. Finally, we consider real data of the cholera outbreak in Yemen, from April 27, 2017 to April 15, 2018, choosing the values of the parameters of the uncontrolled model that fit the real data. Using our optimal control results, we show, numerically, that the distribution of chlorine water tablets could have stopped, in a fast way, the worst cholera outbreak that ever occurred in human history. Due to the critical situation of Yemen, we also simulate the case where only a small percentage of susceptible individuals has access to chlorine water tablets and obtain an optimal control solution that decreases, substantially, the maximum number of infective individuals affected by the outbreak.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10957-020-01668-z</doi><tpages>23</tpages><orcidid>https://orcid.org/0000-0001-7215-5114</orcidid><orcidid>https://orcid.org/0000-0001-8641-2505</orcidid><orcidid>https://orcid.org/0000-0002-7238-546X</orcidid><orcidid>https://orcid.org/0000-0003-4592-3426</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Applications of Mathematics Bifurcations Calculus of Variations and Optimal Control Optimization Chlorine Cholera Computer simulation Disease control Engineering Mathematical models Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimal control Optimization Outbreaks Tablets Theory of Computation Water purification |
| title | Optimal Control of Aquatic Diseases: A Case Study of Yemen’s Cholera Outbreak |
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