On the Integrability of the SIR Epidemic Model with Vital Dynamics
Author
Source
Advances in Mathematical Physics
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-07-06
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
In this paper, we study the SIR epidemic model with vital dynamics Ṡ=−βSI+μN−S,İ=βSI−γ+μI,Ṙ=γI−μR, from the point of view of integrability.
In the case of the death/birth rate μ=0, the SIR model is integrable, and we provide its general solutions by implicit functions, two Lax formulations and infinitely many Hamilton-Poisson realizations.
In the case of μ≠0, we prove that the SIR model has no polynomial or proper rational first integrals by studying the invariant algebraic surfaces.
Moreover, although the SIR model with μ≠0 is not integrable and we cannot get its exact solution, based on the existence of an invariant algebraic surface, we give the global dynamics of the SIR model with μ≠0.
American Psychological Association (APA)
Chen, Ding. 2020. On the Integrability of the SIR Epidemic Model with Vital Dynamics. Advances in Mathematical Physics،Vol. 2020, no. 2020, pp.1-10.
https://search.emarefa.net/detail/BIM-1127439
Modern Language Association (MLA)
Chen, Ding. On the Integrability of the SIR Epidemic Model with Vital Dynamics. Advances in Mathematical Physics No. 2020 (2020), pp.1-10.
https://search.emarefa.net/detail/BIM-1127439
American Medical Association (AMA)
Chen, Ding. On the Integrability of the SIR Epidemic Model with Vital Dynamics. Advances in Mathematical Physics. 2020. Vol. 2020, no. 2020, pp.1-10.
https://search.emarefa.net/detail/BIM-1127439
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1127439