Journal of Applied Mathematics and Computing

, Volume 59, Issue 1–2, pp 305–321 | Cite as

Dynamics of a predator–prey model with harvesting and reserve area for prey in the presence of competition and toxicity

  • Younes LouartassiEmail author
  • Abdellah Alla
  • Khalid Hattaf
  • Aissam Nabil
Original Research


The aim of this paper is to present and study a three-dimensional continuous time dynamical system modeling a predator–prey with harvesting and reserve zone for the prey in the presence of competition and toxicity. We first prove that our model is ecologically and mathematically well-posed. In addition, the stability analysis is investigated by direct and indirect Lyapunov methods. By using the Pontryagin’s maximum principle, an optimal harvesting policy is established. Furthermore, numerical simulations are given in order to illustrate our theoretical results.


Predator–prey model Competition Toxicity Stability Optimal harvesting policy 

Mathematics Subject Classification

34K18 34K20 92B20 


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Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  1. 1.LASTIMI, Superior School of Technology SaléMohammed V University in RabatSaléMorocco
  2. 2.LAMA-ANLIMAD, Faculty of SciencesMohammed V University in RabatRabatMorocco
  3. 3.Centre Régional des Métiers de l’Education et de la Formation (CRMEF)CasablancaMorocco

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