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Communications in Mathematical Biology and Neuroscience ISSN 2052-2541

Archives › Volume 2020 (2020)

Commun. Math. Biol. Neurosci. 2020 (2020), Article ID 2

Analysis of an SIRS epidemic model with nonlinear incidence and vaccination

Baolin Li, Chunyang Qin, Xia Wang

PDF (214.0 KB) https://doi.org/10.28919/cmbn/4262

Abstract

In this paper, we study an SIRS epidemic model with a nonlinear incidence rate and vaccination. We give the existence of positivity, and boundedness of the equilibrium of the model. We calculate the basic reproduction number of the proposed model by using the next generation matrix method. By constructing Lyapunov function, we show that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is less or equal than one and that the endemic equilibrium is globally asymptotically stable when the basic reproduction number is greater than one. Numerical simulations are performed to investigate the effect of vaccinate on model behavior.

Published
17 January 2020
Volume
2020 (2020)
License
CC BY 3.0

Copyright © 2020 Baolin Li, Chunyang Qin, Xia Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this article

B. Li, C. Qin, X. Wang, Analysis of an SIRS epidemic model with nonlinear incidence and vaccination, Commun. Math. Biol. Neurosci. 2020 (2020), 2. https://doi.org/10.28919/cmbn/4262

BibTeX
@article{Li2020,
  author  = {Li, Baolin and Qin, Chunyang and Wang, Xia},
  title   = {Analysis of an SIRS epidemic model with nonlinear incidence and vaccination},
  journal = {Commun. Math. Biol. Neurosci.},
  volume  = {2020},
  year    = {2020},
  pages   = {2},
  doi     = {10.28919/cmbn/4262}
}