Optimal control of HIV/AIDS in the workplace in the presence of careless individuals.
Identifieur interne : 000458 ( Main/Exploration ); précédent : 000457; suivant : 000459Optimal 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
Affiliations:
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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><idno type="wicri:Area/Ncbi/Curation">000683</idno><idno type="wicri:Area/Ncbi/Checkpoint">000683</idno><idno type="wicri:Area/Main/Merge">000458</idno><idno type="wicri:Area/Main/Curation">000458</idno><idno type="wicri:Area/Main/Exploration">000458</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. 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></analytic><series><title level="j">Computational and mathematical methods in medicine</title><idno type="eISSN">1748-6718</idno><imprint><date when="2014" type="published">2014</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Acquired Immunodeficiency Syndrome (prevention & control)</term><term>Acquired Immunodeficiency Syndrome (transmission)</term><term>Algorithms</term><term>Basic Reproduction Number</term><term>Communicable Disease Control (methods)</term><term>Computer Simulation</term><term>HIV Infections (prevention & control)</term><term>HIV Infections (transmission)</term><term>Humans</term><term>Models, Theoretical</term><term>Nonlinear Dynamics</term><term>Occupational Exposure</term><term>Occupational Health</term><term>Workplace</term></keywords><keywords scheme="KwdFr" xml:lang="fr"><term>Algorithmes</term><term>Contrôle des maladies contagieuses ()</term><term>Dynamique non linéaire</term><term>Exposition professionnelle</term><term>Humains</term><term>Infections à VIH ()</term><term>Infections à VIH (transmission)</term><term>Lieu de travail</term><term>Modèles théoriques</term><term>Nombre de reproduction de base</term><term>Santé au travail</term><term>Simulation numérique</term><term>Syndrome d'immunodéficience acquise ()</term><term>Syndrome d'immunodéficience acquise (transmission)</term></keywords><keywords scheme="MESH" qualifier="methods" xml:lang="en"><term>Communicable Disease Control</term></keywords><keywords scheme="MESH" qualifier="prevention & control" xml:lang="en"><term>Acquired Immunodeficiency Syndrome</term><term>HIV Infections</term></keywords><keywords scheme="MESH" qualifier="transmission" xml:lang="en"><term>Acquired Immunodeficiency Syndrome</term><term>HIV Infections</term></keywords><keywords scheme="MESH" xml:lang="en"><term>Algorithms</term><term>Basic Reproduction Number</term><term>Computer Simulation</term><term>Humans</term><term>Models, Theoretical</term><term>Nonlinear Dynamics</term><term>Occupational Exposure</term><term>Occupational Health</term><term>Workplace</term></keywords><keywords scheme="MESH" xml:lang="fr"><term>Algorithmes</term><term>Contrôle des maladies contagieuses</term><term>Dynamique non linéaire</term><term>Exposition professionnelle</term><term>Humains</term><term>Infections à VIH</term><term>Lieu de travail</term><term>Modèles théoriques</term><term>Nombre de reproduction de base</term><term>Santé au travail</term><term>Simulation numérique</term><term>Syndrome d'immunodéficience acquise</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">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.</div></front></TEI><affiliations><list><country><li>Afrique du Sud</li><li>Ghana</li></country></list><tree><country name="Ghana"><noRegion><name sortKey="Seidu, Baba" sort="Seidu, Baba" uniqKey="Seidu B" first="Baba" last="Seidu">Baba Seidu</name></noRegion></country><country name="Afrique du Sud"><noRegion><name sortKey="Makinde, Oluwole D" sort="Makinde, Oluwole D" uniqKey="Makinde O" first="Oluwole D" last="Makinde">Oluwole D. Makinde</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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