Epidemiological models with quadratic equation for endemic equilibria—A bifurcation atlas. (2nd May 2020)

• Record Type: Journal Article
• Authors: Ouifki, Rachid; Banasiak, Jacek
• Other Names: Banasiak Jacek guestEditor.; Lachowicz Mirosław guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 18(2021)
• Page Start: 10413
• Page End: 10429
• Publication Date: 2020-05-02
• Subjects: backward bifurcation -- basic reproductive number -- endemic equilibria -- epidemiological models; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6389
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The existence and occurrence, especially by a backward bifurcation, of endemic equilibria is of utmost importance in determining the spread and persistence of a disease. In many epidemiological models, the equation for the endemic equilibria is quadratic, with the coefficients determined by the parameters of the model. Despite its apparent simplicity, such an equation can describe an amazing number of dynamical behaviors. In this paper, we shall provide a comprehensive survey of possible bifurcation patterns, deriving explicit conditions on the equation's parameters for the occurrence of each of them, and discuss illustrative examples.