Optimal control analysis of a predator-prey model with harvesting and variable carrying capacity

Ibrahim M. Elmojtaba*, Amina Al-Sawaii, Mariam Al-Moqbali

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, we developed and fully analysed a mathematical model for the dynamics of predator and prey where the carrying capacity is considered to be a logistically increasing function of time, and both populations are under harvesting. Our results showed that if the harvesting rate is high then both populations could go to extinction. We also showed that the system undergoes Hopf bifurcation when the harvesting rate of the prey crosses a critical value; in fact the stability of the system changes with the change of the values of the prey harvesting rate. Optimal harvesting is shown to give a high yield and keep both population away from extension.

Original languageEnglish
Article number12
Pages (from-to)1-19
Number of pages19
JournalCommunications in Mathematical Biology and Neuroscience
Publication statusPublished - 2020
Externally publishedYes


  • Hopf bifurcation
  • Local stability
  • Optimal harvesting
  • Predator-prey model
  • Variable carrying capacity

ASJC Scopus subject areas

  • Neuroscience(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Applied Mathematics

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