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Modelling and optimal control of typhoid fever disease with cost-effective strategies

dc.contributor.authorTilahun, Getachew Teshomeen_ZA
dc.contributor.authorMakinde, Oluwole Danielen_ZA
dc.contributor.authorMalonza, Daviden_ZA
dc.date.accessioned2018-08-22T13:42:06Z
dc.date.available2018-08-22T13:42:06Z
dc.date.issued2017-09
dc.identifier.citationTilahun, G. T., Makinde, O. D. & Malonza, D. 2017. Modelling and optimal control of typhoid fever disease with cost-effective strategies. 2324518. doi:10.1155/2017/2324518en_ZA
dc.identifier.isbn1748-670X (print)
dc.identifier.issn1748-6718 (online)
dc.identifier.otherdoi:10.1155/2017/2324518.
dc.identifier.urihttp://hdl.handle.net/10019.1/104331
dc.descriptionCITATION: Tilahun, G. T., Makinde, O. D. & Malonza, D. 2017. Modelling and optimal control of typhoid fever disease with cost-effective strategies. 2324518. doi:10.1155/2017/2324518.en_ZA
dc.descriptionThe original publication is available at https://www.hindawi.com/journals/cmmm/en_ZA
dc.description.abstractWe propose and analyze a compartmental nonlinear deterministic mathematical model for the typhoid fever outbreak and optimal control strategies in a community with varying population.The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. The model exhibits a forward transcritical bifurcation and the sensitivity analysis is performed.The optimal control problem is designed by applying Pontryagin maximum principle with three control strategies, namely, the prevention strategy through sanitation, proper hygiene, and vaccination; the treatment strategy through application of appropriate medicine; and the screening of the carriers. The cost functional accounts for the cost involved in prevention, screening, and treatment together with the total number of the infected persons averted. Numerical results for the typhoid outbreak dynamics and its optimal control revealed that a combination of prevention and treatment is the best cost-effective strategy to eradicate the disease.en_ZA
dc.language.isoen_ZAen_ZA
dc.publisherHindawi Publishing Corporationen_ZA
dc.subjectTyphoid feveren_ZA
dc.subjectDiseasesen_ZA
dc.subjectSalmonellaen_ZA
dc.titleModelling and optimal control of typhoid fever disease with cost-effective strategiesen_ZA
dc.typeArticleen_ZA
dc.description.versionPublisher's versionen_ZA
dc.rights.holderAuthors retain copyrighten_ZA


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