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Communications in Mathematical Biology and Neuroscience ISSN 2052-2541

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Commun. Math. Biol. Neurosci. 2020 (2020), Article ID 17

Backward bifurcation and global stability in a heroin epidemic model

Reza Memarbashi, Somaye Taghavi

PDF (242.1 KB) https://doi.org/10.28919/cmbn/4085

Abstract

In this paper, we propose and study a heroin epidemic model considering the effect of incarceration of users due to criminal actions. We prove the occurrence of backward bifurcation and compute the threshold quantity $R_0^c$ by a new method. Furthermore the global stability of the equilibrium points of the model is investigated using Lyapunov functions and geometric stability method.

Published
16 April 2020
Volume
2020 (2020)
License
CC BY 3.0

Copyright © 2020 Reza Memarbashi, Somaye Taghavi. 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

R. Memarbashi, S. Taghavi, Backward bifurcation and global stability in a heroin epidemic model, Commun. Math. Biol. Neurosci. 2020 (2020), 17. https://doi.org/10.28919/cmbn/4085

BibTeX
@article{Memarbashi2020,
  author  = {Memarbashi, Reza and Taghavi, Somaye},
  title   = {Backward bifurcation and global stability in a heroin epidemic model},
  journal = {Commun. Math. Biol. Neurosci.},
  volume  = {2020},
  year    = {2020},
  pages   = {17},
  doi     = {10.28919/cmbn/4085}
}