Back to Search
Start Over
Stability and bifurcations of an SIR model with a nonlinear incidence rate.
- Source :
- Mathematical Methods in the Applied Sciences; Jun2023, Vol. 46 Issue 9, p10850-10866, 17p
- Publication Year :
- 2023
-
Abstract
- In this paper, an SIR model with a nonlinear incidence rate is studied. A diseaseāfree equilibrium E0$$ {E}_0 $$, an endemic equilibrium E1$$ {E}_1 $$, and the basic reproduction number of the model R0$$ {R}_0 $$ are obtained. If R0<1,E0$$ {R}_0&lt;1,{E}_0 $$ is locally asymptotically stable and if R0>1,E1$$ {R}_0&gt;1,{E}_1 $$ is locally asymptotically stable. By Barbalat's lemma, we study the global stability of the model. Transcritical bifurcation analysis is investigated by using the Sotomayor theorem. As the infection rate increases, the asymptotic behavior of the system near E0$$ {E}_0 $$ approaches E1$$ {E}_1 $$ and the system has a transcritical bifurcation. Also, we check the existence of Hopf bifurcation for the given system. In addition, a sensitivity analysis is provided for the basic reproduction number. Our results are supported with numerical simulations. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01704214
- Volume :
- 46
- Issue :
- 9
- Database :
- Complementary Index
- Journal :
- Mathematical Methods in the Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 163704071
- Full Text :
- https://doi.org/10.1002/mma.9155