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Global analysis of a time fractional order spatio-temporal SIR model
- Source :
- Scientific Reports, Vol 12, Iss 1, Pp 1-13 (2022)
- Publication Year :
- 2022
- Publisher :
- Nature Portfolio, 2022.
-
Abstract
- Abstract We deal in this paper with a diffusive SIR epidemic model described by reaction–diffusion equations involving a fractional derivative. The existence and uniqueness of the solution are shown, next to the boundedness of the solution. Further, it has been shown that the global behavior of the solution is governed by the value of $$R_0$$ R 0 , which is known in epidemiology by the basic reproduction number. Indeed, using the Lyapunov direct method it has been proved that the disease will extinct for $$ R_0 1$$ R 0 > 1 , the disease will persist and the unique positive equilibrium is globally stable. Some numerical illustrations have been used to confirm our theoretical results.
Details
- Language :
- English
- ISSN :
- 20452322
- Volume :
- 12
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Scientific Reports
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.f16b1a8e58f2401aaa514ad815c95abc
- Document Type :
- article
- Full Text :
- https://doi.org/10.1038/s41598-022-08992-6