East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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MATHEMATICAL ANALYSIS OF A THREE-SPECIES HOST-PARASITOID-HYPERPARASITOID

  • LIJIAO JIA (Department of Mathematics, Pusan National University) ;
  • YUNIL ROH (Department of Mathematics, Pusan National University) ;
  • IL HYO JUNG (Department of Mathematics, Institute of Mathematical Science, Finance Fishery Manufacture Industrial Mathematics Center on BigData, Pusan National University)
  • Received : 2024.05.14
  • Accepted : 2024.06.18
  • Published : 2024.09.30
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Abstract

This study investigated a new three-species host-parasitoid-hyperparasitoid system, which considers the mutual interference functional response. We establish the existence and uniqueness of positive equilibrium points and demonstrate that the presence of hyperparasitoids always leads to an increase in the level of host population equilibrium. In addition, we demonstrate that the quest constant b of hyperparasitoids is proportional to the host equilibrium level, which is critical for the efficiency of biological control programs. We provide parametric conditions for the local stability of the proposed system. Some numerical simulations are performed to validate our theoretical results.

Keywords

Acknowledgement

This work was supported by a 2-Year Research Grant of Pusan National University.

References

  1. Q. Din, Neimark-Sacker bifurcation and chaos control in Hassell-Varley model, J. Differ. Equations. 23 (2017), no. 4, 741-762.
  2. J. R. Beddington and P. S. Hammond, On the dynamics of host-parasite-hyperparasite interactions, The Journal of Animal Ecology. (1977), 811-821.
  3. L. Zhang and M. Zhao, Dynamic complexities in a hyperparasitic system with prolonged diapause for host, Chaos Soliton. & Fract. 42 (2009), no. 2, 1136-1142.
  4. S. S. Schooler, P. De Barro, and A. R. Ives, The potential for hyperparasitism to compromise biological control: Why don't hyperparasitoids drive their primary parasitoid hosts extinct?, Biol. Control. 58 (2011), no. 3, 167-173.
  5. H. J. Broadley, E. A. Kelly, J. S. Elkinton, R. R. Kula, and G. H. Boettner, Identification and impact of hyperparasitoids and predators affecting Cyzenis albicans (Tachinidae), a recently introduced biological control agent of winter moth (Operophtera brumata L.) in the northeastern USA, Biol. Control. 121 (2018), 99-108.
  6. R. M. May and M. P. Hassell, The dynamics of multiparasitoid-host interactions, The American Naturalist. 117 (1981), no. 3, 234-261.
  7. L. Allen, An introduction to mathematical biology, Prentice Hall, New Jersey, 2007.
  8. X. Li, C. Mou, W. Niu, and D. Wang, Stability analysis for discrete biological models using algebraic methods, Mathematics in Computer Science. 5 (2011), 247-262.
  9. A. Singh, Attack by a common parasitoid stabilizes population dynamics of multi-host communities, J. Theor. Biol. 531 (2021), Article ID 110897.
  10. E. H. Poelman, A. Cusumano, and J. G. De Boer, The ecology of hyperparasitoids, Annual Review of Entomology. 67 (2022), 143-161.
  11. P. Wu, B. Ma, S. Yan, J. Xu, and R. Zhang, The hyperparasitoid Marietta picta (Hymenoptera: Aphelinidae) mediates competitive interactions between two parasitoids of Paratrioza sinica (Hemiptera: Psyllidae): Tamarixia lyciumi (Hymenoptera: Eulophidae) and Psyllaephagus arenarius (Hymenoptera: Encyrtidae), Biol. Control. 126 (2018), 169-176.