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Communications in Mathematical Biology and Neuroscience ISSN 2052-2541

Archives › Volume 2019 (2019)

Commun. Math. Biol. Neurosci. 2019 (2019), Article ID 15

Extinction and persistence of a stochastic SIS epidemic model with vertical transmission, specific functional response and Levy jumps

Mouhcine Naim, Fouad Lahmidi, Abdelwahed Namir

PDF (175.1 KB) https://doi.org/10.28919/cmbn/3905

Abstract

In this paper, we study the dynamics of a stochastic SIS epidemic model with vertical transmission and specific functional response. The environment variability in this work is characterized by Gaussian white noise and Levy jump noise. We establish the existence and uniqueness of a global positive solution starting from any positive initial value. We also investigate extinction and persistence in mean of the disease. Numerical examples are presented to illustrate the theoretical results.

Published
3 June 2019
Volume
2019 (2019)
License
CC BY 3.0

Copyright © 2019 Mouhcine Naim, Fouad Lahmidi, Abdelwahed Namir. 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

M. Naim, F. Lahmidi, A. Namir, Extinction and persistence of a stochastic SIS epidemic model with vertical transmission, specific functional response and Levy jumps, Commun. Math. Biol. Neurosci. 2019 (2019), 15. https://doi.org/10.28919/cmbn/3905

BibTeX
@article{Naim2019,
  author  = {Naim, Mouhcine and Lahmidi, Fouad and Namir, Abdelwahed},
  title   = {Extinction and persistence of a stochastic SIS epidemic model with vertical transmission, specific functional response and Levy jumps},
  journal = {Commun. Math. Biol. Neurosci.},
  volume  = {2019},
  year    = {2019},
  pages   = {15},
  doi     = {10.28919/cmbn/3905}
}