Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity

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dc.contributor.authorOkosun K.O.
dc.contributor.authorOuifki R.
dc.contributor.authorMarcus N.
dc.date.accessioned2011-10-13T16:59:10Z
dc.date.available2011-10-13T16:59:10Z
dc.date.issued2011-10-13
dc.description.abstractWe derive and analyse a deterministic model for the transmission of malaria disease with mass action form of infection. Firstly, we calculate the basic reproduction number, R0, and investigate the existence and stability of equilibria. The system is found to exhibit backward bifurcation. The implication of this occurrence is that the classical epidemiological requirement for effective eradication of malaria, R0 < 1, is no longer sufficient, even though necessary. Secondly, by using optimal control theory we derive the conditions under which it is optimal to eradicate the disease and examine the impact of a possible combined vaccination and treatment strategy on the disease transmission. When eradication is impossible, we derive the necessary conditions for optimal control of the disease using Pontryagin's Maximum Principle. The results obtained from the numerical simulations of the model show that a possible vaccination combined with effective treatment regime would reduce the spread of the disease appreciably. Crown Copyright © 2011.
dc.description.versionArticle in Press
dc.identifier.citationBioSystems
dc.identifier.citationhttp://www.scopus.com/inward/record.url?eid=2-s2.0-80052101612&partnerID=40&md5=91ec638936851599e46291e35eef50ad
dc.identifier.issn3032647
dc.identifier.other10.1016/j.biosystems.2011.07.006
dc.identifier.urihttp://hdl.handle.net/10019.1/17004
dc.titleOptimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity
dc.typeArticle in Press
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