Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 43, Issue 18, Pages 10413-10429Publisher
WILEY
DOI: 10.1002/mma.6389
Keywords
backward bifurcation; basic reproductive number; endemic equilibria; epidemiological models
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Funding
- DST/NRF SARChI Chair in Mathematical Models and Methods in Biosciences and Bioengineering at the University of Pretoria [82770]
- National Science Centre of Poland [2017/25/B/ST1/00051]
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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.
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