Modelling and optimal control of pneumonia disease with cost-effective strategies

dc.contributor.authorTilahun, Getachew Teshomeen_ZA
dc.contributor.authorMakinde, Oluwole Danielen_ZA
dc.contributor.authorMalonza, Daviden_ZA
dc.date.accessioned2019-02-14T10:31:20Z
dc.date.available2019-02-14T10:31:20Z
dc.date.issued2017
dc.descriptionCITATION: Tilahun, G. T., Makinde, O. D. & Malonza, D. 2017. Modelling and optimal control of pneumonia disease with cost-effective strategies. Journal of Biological Dynamics, 11(S2):400-426, doi:10.1080/17513758.2017.1337245.
dc.descriptionThe original publication is available at https://www.tandfonline.com
dc.description.abstractWe propose and analyse a nonlinear mathematical model for the transmission dynamics of pneumonia disease in a population of varying size. The deterministic compartmental model is studied using stability theory of differential equations. The effective reproduction number is obtained and also the asymptotic stability conditions for the disease free and as well as for the endemic equilibria are established. The possibility of bifurcation of the model and the sensitivity indices of the basic reproduction number to the key parameters are determined. Using Pontryagin's maximum principle, the optimal control problem is formulated with three control strategies: namely disease prevention through education, treatment and screening. The cost-effectiveness analysis of the adopted control strategies revealed that the combination of prevention and treatment is the most cost-effective intervention strategies to combat the pneumonia pandemic. Numerical simulation is performed and pertinent results are displayed graphically.en_ZA
dc.description.urihttps://www.tandfonline.com/doi/full/10.1080/17513758.2017.1337245
dc.description.versionPublisher's version
dc.format.extent28 pages
dc.identifier.citationTilahun, G. T., Makinde, O. D. & Malonza, D. 2017. Modelling and optimal control of pneumonia disease with cost-effective strategies. Journal of Biological Dynamics, 11(S2):400-426, doi:10.1080/17513758.2017.1337245
dc.identifier.issn1751-3766 (online)
dc.identifier.issn1751-3758 (print)
dc.identifier.otherdoi:10.1080/17513758.2017.1337245
dc.identifier.urihttp://hdl.handle.net/10019.1/105414
dc.language.isoen_ZAen_ZA
dc.publisherInforma UK Limited, trading as Taylor & Francis Group
dc.rights.holderAuthors retain copyright
dc.subjectPneumoniaen_ZA
dc.subjectPulmonary fibrosisen_ZA
dc.subjectPneumonia, Pneumococcalen_ZA
dc.titleModelling and optimal control of pneumonia disease with cost-effective strategiesen_ZA
dc.typeArticleen_ZA
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