Epidemiological models with quadratic equation for endemic equilibria—a bifurcation atlas
| dc.contributor.author | Ouifki, Rachid | |
| dc.contributor.author | Banasiak, Jacek | |
| dc.contributor.email | rachid.ouifki@up.ac.za | en_ZA |
| dc.date.accessioned | 2021-09-16T15:08:34Z | |
| dc.date.available | 2021-09-16T15:08:34Z | |
| dc.date.issued | 2020-12 | |
| dc.description.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. | en_ZA |
| dc.description.department | Mathematics and Applied Mathematics | en_ZA |
| dc.description.sponsorship | The DST/NRF SARChI Chair in Mathematical Models and Methods in Biosciences and Bioengineering at the University of Pretoria and National Science Centre of Poland. | en_ZA |
| dc.description.uri | http://wileyonlinelibrary.com/journal/mma | en_ZA |
| dc.identifier.citation | Ouifki, R. & Banasiak, J. 2020, 'Epidemiological models with quadratic equation for endemic equilibria—A bifurcation atlas', Mathematical Methods in the Applied Sciences, vol. 43, no. 18, pp. 10413-10429. | en_ZA |
| dc.identifier.issn | 0170-4214 (print) | |
| dc.identifier.issn | 1099-1476 (online) | |
| dc.identifier.other | 10.1002/mma.6389 | |
| dc.identifier.uri | http://hdl.handle.net/2263/81889 | |
| dc.language.iso | en | en_ZA |
| dc.publisher | Wiley | en_ZA |
| dc.rights | © 2020 John Wiley and Sons, Ltd. This is the pre-peer rev'Epidemiological models with quadratic equation for endemic equilibria—A bifurcation atlas', Mathematical Methods in the Applied Sciences, vol. 43, no. 18, pp. 10413-10429, 2020, doi : 10.1002/mma.6389. The definite version is available at : http://wileyonlinelibrary.com/journal/mma. | en_ZA |
| dc.subject | Backward bifurcation | en_ZA |
| dc.subject | Basic reproductive number | en_ZA |
| dc.subject | Endemic equilibria | en_ZA |
| dc.subject | Epidemiological models | en_ZA |
| dc.title | Epidemiological models with quadratic equation for endemic equilibria—a bifurcation atlas | en_ZA |
| dc.type | Postprint Article | en_ZA |