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Journal of Mathematical Biology

, Volume 79, Issue 6–7, pp 2183–2209 | Cite as

Stochastic plant–herbivore interaction model with Allee effect

  • Manalebish Debalike AsfawEmail author
  • Semu Mitiku Kassa
  • Edward M. Lungu
Article
  • 164 Downloads

Abstract

Environmental noises often affect population dynamics, and hence many benefits are gained in using stochastic models since real life is full of stochasticity and randomness. In this paper a stochastic extension of a model by Asfaw et al. (Int J Biomath 11:1850057, 2018) is considered. Due to the non-linearity of the model, first, a simplified stochastic plant–herbivore model is formulated and analyzed for its global Lipschitz continuity, positivity, existence and uniqueness of solutions. Second, the analysis is extended to a more complex and realistic model. Numerical simulations using Euler–Maruyama method are employed to demonstrate the long term dynamics. It was found that the noise added to the herbivore population resulted more change in the dynamics than the noise added to the plant population (food source). Ignoring the environmental noise could make the land management and wild life conservation not to maintain their goals.

Keywords

Plant–herbivore model Stochastic Allee effect Harvest 

Mathematics Subject Classification

34F05 60H10 91B70 92B05 92D40 

Notes

Acknowledgements

This work is partially supported by The Simon’s Foundation project based in Botswana International University of Science and Technology. M.D.A. would like to thank the Organization for Women in Science for the Developing World (OWSD) and Swedish International Development Cooperation Agency (SIDA), the International Science Program project based at Addis Ababa University for the support she receives during the preparation of the manuscript.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsAddis Ababa UniversityAddis AbabaEthiopia
  2. 2.Department of Mathematics and Statistical SciencesBotswana International University of Science and Technology (BIUST)PalapyeBotswana

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