Backward bifurcation analysis for two continuous and discrete epidemiological models 

dc.contributor.authorAnguelov, Roumen
dc.contributor.authorDukuza, Njengele Kenneth Kennedy
dc.contributor.authorLubuma, Jean M.-S.
dc.contributor.emailkenneth.dukuza@up.ac.zaen_ZA
dc.date.accessioned2019-05-17T06:58:04Z
dc.date.issued2018-12
dc.description.abstractThe bifurcation analysis of a continuous n‐dimensional nonlinear dynamical system with a nonhyperbolic equilibrium point is done by using the main theorem in the work of Castillo‐Chavez and Song. We derive an analog of this theorem for discrete dynamical systems. We design nonstandard finite difference schemes for a susceptible‐infectious‐susceptible epidemiological model with vaccination and for a malaria model. For the latter model, we sharpen the interval of the values of the disease induced death rate for which backward bifurcation may occur. Applying the discrete theorem, it is shown that each nonstandard finite difference scheme replicates the property of the continuous model of having backward bifurcation at the value one of the basic reproduction number.en_ZA
dc.description.departmentMathematics and Applied Mathematicsen_ZA
dc.description.embargo2019-12-01
dc.description.librarianhj2019en_ZA
dc.description.sponsorshipThe Department of Science and Technology (DST)/National Research Foundation (NRF) South African Research Chairs Initiative (SARChI) Chair in Mathematical Models and Methods in Bioengineering and Biosciences.en_ZA
dc.description.urihttp://wileyonlinelibrary.com/journal/mmaen_ZA
dc.identifier.citationAnguelov R, Dukuza K, Lubuma JM-S. Backward bifurcation analy-sis for two continuous and discrete epidemiological models. Mathematical Methods in the Applied Sciences. 2018;41:8784–8798.https://doi.org/10.1002/mma.5138.en_ZA
dc.identifier.issn0170-4214 (print)
dc.identifier.issn1099-1476 (online)
dc.identifier.issn10.1002/mma.5138
dc.identifier.urihttp://hdl.handle.net/2263/69154
dc.language.isoenen_ZA
dc.publisherWileyen_ZA
dc.rights© 2018 John Wiley and Sons, Ltd. This is the pre-peer reviewed version of the following article : Backward bifurcation analy-sis for two continuous and discrete epidemiological models. Mathematical Methods in the Applied Sciences. 2018;41:8784–8798.https://doi.org/10.1002/mma.5138. The definite version is available at : http://wileyonlinelibrary.com/journal/mma.en_ZA
dc.subjectBifurcation analysisen_ZA
dc.subjectCenter manifold theoryen_ZA
dc.subjectEpidemiological modelen_ZA
dc.subjectReproductive numberen_ZA
dc.titleBackward bifurcation analysis for two continuous and discrete epidemiological models en_ZA
dc.typePostprint Articleen_ZA

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