Optimal control of HIV/AIDS in the workplace in the presence of careless individuals.
Identifieur interne : 000683 ( Ncbi/Merge ); précédent : 000682; suivant : 000684Optimal control of HIV/AIDS in the workplace in the presence of careless individuals.
Auteurs : Baba Seidu [Ghana] ; Oluwole D. Makinde [Afrique du Sud]Source :
- Computational and mathematical methods in medicine [ 1748-6718 ] ; 2014.
Descripteurs français
- KwdFr :
- Algorithmes, Contrôle des maladies contagieuses (), Dynamique non linéaire, Exposition professionnelle, Humains, Infections à VIH (), Infections à VIH (transmission), Lieu de travail, Modèles théoriques, Nombre de reproduction de base, Santé au travail, Simulation numérique, Syndrome d'immunodéficience acquise (), Syndrome d'immunodéficience acquise (transmission).
- MESH :
English descriptors
- KwdEn :
- Acquired Immunodeficiency Syndrome (prevention & control), Acquired Immunodeficiency Syndrome (transmission), Algorithms, Basic Reproduction Number, Communicable Disease Control (methods), Computer Simulation, HIV Infections (prevention & control), HIV Infections (transmission), Humans, Models, Theoretical, Nonlinear Dynamics, Occupational Exposure, Occupational Health, Workplace.
- MESH :
- methods : Communicable Disease Control.
- prevention & control : Acquired Immunodeficiency Syndrome, HIV Infections.
- transmission : Acquired Immunodeficiency Syndrome, HIV Infections.
- Algorithms, Basic Reproduction Number, Computer Simulation, Humans, Models, Theoretical, Nonlinear Dynamics, Occupational Exposure, Occupational Health, Workplace.
Abstract
A nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics of HIV/AIDS in the workplace. The disease-free equilibrium point of the model is shown to be locally asymptotically stable if the basic reproductive number, ℛ0, is less than unity and the model is shown to exhibit a unique endemic equilibrium when the basic reproductive number is greater than unity. It is shown that, in the absence of recruitment of infectives, the disease is eradicated when ℛ0 < 1, whiles the disease is shown to persist in the presence of recruitment of infected persons. The basic model is extended to include control efforts aimed at reducing infection, irresponsibility, and nonproductivity at the workplace. This leads to an optimal control problem which is qualitatively analyzed using Pontryagin's Maximum Principle (PMP). Numerical simulation of the resulting optimal control problem is carried out to gain quantitative insights into the implications of the model. The simulation reveals that a multifaceted approach to the fight against the disease is more effective than single control strategies.
DOI: 10.1155/2014/831506
PubMed: 25097663
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Makinde</name><affiliation wicri:level="1"><nlm:affiliation>Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa.</nlm:affiliation><country xml:lang="fr">Afrique du Sud</country><wicri:regionArea>Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395</wicri:regionArea><wicri:noRegion>Saldanha 7395</wicri:noRegion></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PubMed</idno><date when="2014">2014</date><idno type="RBID">pubmed:25097663</idno><idno type="pmid">25097663</idno><idno type="doi">10.1155/2014/831506</idno><idno type="wicri:Area/PubMed/Corpus">000131</idno><idno type="wicri:explorRef" wicri:stream="PubMed" wicri:step="Corpus" wicri:corpus="PubMed">000131</idno><idno type="wicri:Area/PubMed/Curation">000131</idno><idno type="wicri:explorRef" wicri:stream="PubMed" wicri:step="Curation">000131</idno><idno type="wicri:Area/PubMed/Checkpoint">000131</idno><idno type="wicri:explorRef" wicri:stream="Checkpoint" wicri:step="PubMed">000131</idno><idno type="wicri:Area/Ncbi/Merge">000683</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Optimal control of HIV/AIDS in the workplace in the presence of careless individuals.</title><author><name sortKey="Seidu, Baba" sort="Seidu, Baba" uniqKey="Seidu B" first="Baba" last="Seidu">Baba Seidu</name><affiliation wicri:level="1"><nlm:affiliation>Applied Mathematics Department, Faculty of Mathematical Sciences, University for Development, Navrongo, Ghana.</nlm:affiliation><country xml:lang="fr">Ghana</country><wicri:regionArea>Applied Mathematics Department, Faculty of Mathematical Sciences, University for Development, Navrongo</wicri:regionArea><wicri:noRegion>Navrongo</wicri:noRegion></affiliation></author><author><name sortKey="Makinde, Oluwole D" sort="Makinde, Oluwole D" uniqKey="Makinde O" first="Oluwole D" last="Makinde">Oluwole D. 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The disease-free equilibrium point of the model is shown to be locally asymptotically stable if the basic reproductive number, ℛ0, is less than unity and the model is shown to exhibit a unique endemic equilibrium when the basic reproductive number is greater than unity. It is shown that, in the absence of recruitment of infectives, the disease is eradicated when ℛ0 < 1, whiles the disease is shown to persist in the presence of recruitment of infected persons. The basic model is extended to include control efforts aimed at reducing infection, irresponsibility, and nonproductivity at the workplace. This leads to an optimal control problem which is qualitatively analyzed using Pontryagin's Maximum Principle (PMP). Numerical simulation of the resulting optimal control problem is carried out to gain quantitative insights into the implications of the model. The simulation reveals that a multifaceted approach to the fight against the disease is more effective than single control strategies.</div></front></TEI><pubmed><MedlineCitation Status="MEDLINE" Owner="NLM"><PMID Version="1">25097663</PMID><DateCreated><Year>2014</Year><Month>08</Month><Day>06</Day></DateCreated><DateCompleted><Year>2015</Year><Month>03</Month><Day>30</Day></DateCompleted><DateRevised><Year>2017</Year><Month>02</Month><Day>20</Day></DateRevised><Article PubModel="Print-Electronic"><Journal><ISSN IssnType="Electronic">1748-6718</ISSN><JournalIssue CitedMedium="Internet"><Volume>2014</Volume><PubDate><Year>2014</Year></PubDate></JournalIssue><Title>Computational and mathematical methods in medicine</Title><ISOAbbreviation>Comput Math Methods Med</ISOAbbreviation></Journal><ArticleTitle>Optimal control of HIV/AIDS in the workplace in the presence of careless individuals.</ArticleTitle><Pagination><MedlinePgn>831506</MedlinePgn></Pagination><ELocationID EIdType="doi" ValidYN="Y">10.1155/2014/831506</ELocationID><Abstract><AbstractText>A nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics of HIV/AIDS in the workplace. The disease-free equilibrium point of the model is shown to be locally asymptotically stable if the basic reproductive number, ℛ0, is less than unity and the model is shown to exhibit a unique endemic equilibrium when the basic reproductive number is greater than unity. It is shown that, in the absence of recruitment of infectives, the disease is eradicated when ℛ0 < 1, whiles the disease is shown to persist in the presence of recruitment of infected persons. The basic model is extended to include control efforts aimed at reducing infection, irresponsibility, and nonproductivity at the workplace. This leads to an optimal control problem which is qualitatively analyzed using Pontryagin's Maximum Principle (PMP). Numerical simulation of the resulting optimal control problem is carried out to gain quantitative insights into the implications of the model. The simulation reveals that a multifaceted approach to the fight against the disease is more effective than single control strategies.</AbstractText></Abstract><AuthorList CompleteYN="Y"><Author ValidYN="Y"><LastName>Seidu</LastName><ForeName>Baba</ForeName><Initials>B</Initials><Identifier Source="ORCID">0000-0001-5652-2690</Identifier><AffiliationInfo><Affiliation>Applied Mathematics Department, Faculty of Mathematical Sciences, University for Development, Navrongo, Ghana.</Affiliation></AffiliationInfo></Author><Author ValidYN="Y"><LastName>Makinde</LastName><ForeName>Oluwole D</ForeName><Initials>OD</Initials><Identifier Source="ORCID">0000-0003-4550-9591</Identifier><AffiliationInfo><Affiliation>Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa.</Affiliation></AffiliationInfo></Author></AuthorList><Language>eng</Language><PublicationTypeList><PublicationType UI="D016428">Journal 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Version="1">7996863</PMID></CommentsCorrections><CommentsCorrections RefType="Cites"><RefSource>BMJ. 2002 Jan 26;324(7331):232-4</RefSource><PMID Version="1">11809650</PMID></CommentsCorrections><CommentsCorrections RefType="Cites"><RefSource>BMJ. 2004 Jul 17;329(7458):129</RefSource><PMID Version="1">15258052</PMID></CommentsCorrections><CommentsCorrections RefType="Cites"><RefSource>Math Biosci Eng. 2004 Sep;1(2):223-41</RefSource><PMID Version="1">20369969</PMID></CommentsCorrections><CommentsCorrections RefType="Cites"><RefSource>IMA J Math Appl Med Biol. 1986;3(4):229-63</RefSource><PMID Version="1">3453839</PMID></CommentsCorrections><CommentsCorrections RefType="Cites"><RefSource>J Biol Phys. 2013 Jan;39(1):99-121</RefSource><PMID Version="1">23860836</PMID></CommentsCorrections><CommentsCorrections RefType="Cites"><RefSource>Biosystems. 2011 Apr;104(1):32-41</RefSource><PMID Version="1">21219965</PMID></CommentsCorrections><CommentsCorrections RefType="Cites"><RefSource>Lancet. 1990 Jul 28;336(8709):221-4</RefSource><PMID Version="1">1973779</PMID></CommentsCorrections><CommentsCorrections RefType="Cites"><RefSource>Math Biosci. 1997 Oct 1;145(1):27-46</RefSource><PMID Version="1">9271894</PMID></CommentsCorrections><CommentsCorrections RefType="Cites"><RefSource>J Theor Biol. 2009 Sep 21;260(2):220-9</RefSource><PMID Version="1">19501107</PMID></CommentsCorrections><CommentsCorrections RefType="Cites"><RefSource>Health Educ Res. 2006 Aug;21(4):567-97</RefSource><PMID Version="1">16847044</PMID></CommentsCorrections></CommentsCorrectionsList><MeshHeadingList><MeshHeading><DescriptorName UI="D000163" MajorTopicYN="N">Acquired Immunodeficiency Syndrome</DescriptorName><QualifierName UI="Q000517" MajorTopicYN="Y">prevention & control</QualifierName><QualifierName UI="Q000635" MajorTopicYN="Y">transmission</QualifierName></MeshHeading><MeshHeading><DescriptorName UI="D000465" MajorTopicYN="N">Algorithms</DescriptorName></MeshHeading><MeshHeading><DescriptorName 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