Analysis and dynamically consistent numerical schemes for the SIS model and related reaction diffusion equation

dc.contributor.authorLubuma, Jean
dc.contributor.authorMureithi, Eunice
dc.contributor.authorTerefe, Yibeltal
dc.date.accessioned2018-11-08T10:20:08Z
dc.date.available2018-11-08T10:20:08Z
dc.date.issued2011
dc.description.abstractThe classical SIS epidemiological model is extended in two directions: (a) The number of adequate contacts per infective in unit time is assumed to be a function of the total population in such a way that this number grows less rapidly as the total population increases; (b) A diffusion term is added to the SIS model and this leads to a reaction diffusion equation, which governs the spatial spread of the disease. With the parameter R0 representing the basic reproduction number, it is shown that R0 = 1 is a forward bifurcation for the model (a), with the disease-free equilibrium being globally asymptotic stable when R0 is less than 1. In the case when R0 is greater than 1, traveling wave solutions are found for the model (b). Nonstandard finite difference (NSFD) schemes that replicate the dynamics of the continuous models are presented. In particular, for the model (a), a nonstandard version of the Runge-Kutta method having high order of convergence is investigated. Numerical experiments that support the theory are provided.en_US
dc.identifier.isbn978-0-7354-0976-7
dc.identifier.urihttp://hdl.handle.net/20.500.11810/4985
dc.language.isoenen_US
dc.publisherProceedings of the 3rd International Conference on Applied Mathematics in Technical and Natural Sciences,(AMiTaNS’11), (Albena, Bulgaria), Institute of Physics-AIP Conf. Proc.en_US
dc.subjectEpidemiological models, local/global stability, nonstandard finite difference scheme, reaction diffusionen_US
dc.titleAnalysis and dynamically consistent numerical schemes for the SIS model and related reaction diffusion equationen_US
dc.typeJournal Article, Peer Revieweden_US
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