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On the nonstandard numerical discretization of SIR epidemic model with a saturated incidence rate and vaccination
- Source :
- AIMS Mathematics, Vol 6, Iss 1, Pp 141-155 (2021)
- Publication Year :
- 2021
- Publisher :
- AIMS Press, 2021.
-
Abstract
- Recently, Hoang and Egbelowo (Boletin de la Sociedad Matematica Mexicana, 2020) proposed a nonstandard finite difference scheme (NSFD) to get a discrete SIR epidemic model with saturated incidence rate and constant vaccination. The discrete model was derived by discretizing the right-hand sides of the system locally and the first order derivative is approximated by the generalized forward difference method but with a restrictive denominator function. Their analysis showed that the NSFD scheme is dynamically-consistent only for relatively small time-step sizes. In this paper, we propose and analyze an alternative NSFD scheme by applying nonlocal approximation and choosing the denominator function such that the proposed scheme preserves the boundedness of solutions. It is verified that the proposed discrete model is dynamically-consistent with the corresponding continuous model for all time-step size. The analytical results have been confirmed by some numerical simulations. We also show numerically that the proposed NSFD scheme is superior to the Euler method and the NSFD method proposed by Hoang and Egbelowo (2020).
- Subjects :
- Lyapunov function
Discretization
Continuous modelling
General Mathematics
lcsh:Mathematics
Finite difference
dynamically-consistent discretization
Function (mathematics)
Nonstandard finite difference scheme
saturated incidence rate
local and global stability analysis
lcsh:QA1-939
Euler method
symbols.namesake
symbols
Applied mathematics
sir epidemic model
Epidemic model
lyapunov function
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 6
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- AIMS Mathematics
- Accession number :
- edsair.doi.dedup.....facffa8b51f21b3af9a364f0ac97e65b