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Bifurcations of an SIRS epidemic model with a general saturated incidence rate
- Source :
- Mathematical Biosciences and Engineering, Vol 19, Iss 11, Pp 10710-10730 (2022)
- Publication Year :
- 2022
- Publisher :
- AIMS Press, 2022.
-
Abstract
- This paper is concerned with the bifurcations of a susceptible-infectious-recovered-susceptible (SIRS) epidemic model with a general saturated incidence rate $ k I^p/(1+\alpha I^p) $. For general $ p > 1 $, it is shown that the model can undergo saddle-node bifurcation, Bogdanov-Takens bifurcation of codimension two, and degenerate Hopf bifurcation of codimension two with the change of parameters. Combining with the results in [1] for $ 0 < p\leq 1 $, this type of SIRS model has Hopf cyclicity $ 2 $ for any $ p > 0 $. These results also improve some previous ones in [2] and [3], which are dealt with the special case of $ p = 2 $.
Details
- Language :
- English
- ISSN :
- 15510018
- Volume :
- 19
- Issue :
- 11
- Database :
- Directory of Open Access Journals
- Journal :
- Mathematical Biosciences and Engineering
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.593aa767e9d447919830b9416d27fe09
- Document Type :
- article
- Full Text :
- https://doi.org/10.3934/mbe.2022501?viewType=HTML