Backward bifurcation analysis for two continuous and discrete epidemiological models. (12th July 2018)

• Record Type: Journal Article
• Authors: Anguelov, Roumen; Dukuza, Kenneth; Lubuma, Jean M.‐S.
• Other Names: Anguelov Roumen guestEditor.; Banasiak Jacek guestEditor.; Debbouche Amar guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 18(2018)
• Page Start: 8784
• Page End: 8798
• Publication Date: 2018-07-12
• Subjects: bifurcation analysis -- center manifold theory -- epidemiological model -- reproductive number; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5138
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The 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.