A mathematical model for Ebola epidemic with self-protection measures

dc.contributor.authorTsanou, Berge
dc.contributor.authorChapwanya, Michael
dc.contributor.authorLubuma, Jean M.-S.
dc.contributor.authorTerefe, Yibeltal Adane
dc.contributor.emailjean.lubuma@up.ac.zaen_ZA
dc.date.accessioned2018-11-02T06:57:10Z
dc.date.issued2018-03
dc.description.abstractA mathematical model presented in Berge T, Lubuma JM-S, Moremedi GM, Morris N Shava RK, A simple mathematical model for Ebola in Africa, J Biol Dyn 11(1): 42–74 (2016) for the transmission dynamics of Ebola virus is extended to incorporate vaccination and change of behavior for self-protection of susceptible individuals. In the new setting, it is shown that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number R0 is less than or equal to unity and unstable when R0>1. In the latter case, the model system admits at least one endemic equilibrium point, which is locally asymptotically stable. Using the parameters relevant to the transmission dynamics of the Ebola virus disease, we give sensitivity analysis of the model. We show that the number of infectious individuals is much smaller than that obtained in the absence of any intervention. In the case of the mass action formulation with vaccination and education, we establish that the number of infectious individuals decreases as the intervention efforts increase. In the new formulation, apart from supporting the theory, numerical simulations of a nonstandard finite difference scheme that we have constructed suggests that the results on the decrease of the number of infectious individuals is valid.en_ZA
dc.description.departmentMathematics and Applied Mathematicsen_ZA
dc.description.embargo2019-03-01
dc.description.librarianhj2018en_ZA
dc.description.sponsorshipThe South African Research Chairs Initiative of the Department of Science and Technology and National Research Foundation: SARChI Chair in Mathematical Models and Methods in Bioengineering and Biosciences. TB and YAT acknowledge the support, in part, of DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS).en_ZA
dc.description.urihttps://www.worldscientific.com/worldscinet/jbsen_ZA
dc.identifier.citationBerge, T., Chapwanya, M., Lubuma, J.M.-S. & Terefe, Y.A. 2018, 'A mathematical model for Ebola epidemic with self-protection measures', Journal of Biological Systems, vol. 26, no. 1, pp. 107-131.en_ZA
dc.identifier.issn0218-3390 (print)
dc.identifier.issn1793-6470 (online)
dc.identifier.other10.1142/S0218339018500067
dc.identifier.urihttp://hdl.handle.net/2263/67130
dc.language.isoenen_ZA
dc.publisherWorld Scientific Publishingen_ZA
dc.rights© 2018 World Scientific Publishing Companyen_ZA
dc.subjectEbola virus disease (EVD)en_ZA
dc.subjectDynamical systemsen_ZA
dc.subjectBehavior changeen_ZA
dc.subjectSensitivity analysisen_ZA
dc.subjectNonstandard finite difference methoden_ZA
dc.subjectNumberen_ZA
dc.subjectDynamicsen_ZA
dc.subjectEnvironmenten_ZA
dc.subjectVirus diseasesen_ZA
dc.subjectGlobal stabilityen_ZA
dc.titleA mathematical model for Ebola epidemic with self-protection measuresen_ZA
dc.typePostprint Articleen_ZA

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