A Stage-structure Leslie-Gower Model with Linear Harvesting and Disease in Predator

Lazarus Kalvein Beay, Zeth Arthur Leleury, Monalisa E. Rijoly, Yopi Andry Lesnussa, Abraham Zacaria Wattimena, Dorteus Lodewyik Rahakbauw


The growth dynamics of various species are affected by various aspects. Harvesting interventions and the spread of disease in species are two important aspects that affect population dynamics and it can be studied. In this work, we consider a stage-structure Leslie–Gower model with linear harvesting on the both prey and predator. Additionally, we also consider the infection aspect in the predator population. The population is divided into four subpopulations: immature prey, mature prey, susceptible predator, and infected predator. We analyze the existences and stabilities of feasible equilibrium points. Our results shown that the harvesting in prey and the disease in predator impacts the behavioral of system. The situation in the system is more complex due to disease in the predator population. Some numerical simulations are given to confirm our results.


Leslie-Gower model; Stage–structure; Linear harvesting; Diseases.

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S. Chen and J. Shi, “Global dynamics of the diffusive Lotka-Volterra competition model with stage structure,” Calculus of Variations and Partial Differential Equations, vol. 59, no. 1, p. 33, 2020. DOI:10.1007/s00526-019-1693-y

X. Zhao and R. Yuan, “Propagation dynamics of a Lotka-Volterra competition model with stage structure in time space periodic environment,” Nonlinear Analysis: Real World Applications, vol. 67, no. 1, p. 103575, 2022. DOI:10.1016/j.nonrwa.2022.103575

L. Ma, J. Gao, D. Li, and W. Lian, “Dynamics of a delayed Lotka-Volterra competition model with directed dispersal,” Nonlinear Analysis: Real World Applications, vol. 71, p. 103830, 2023. DOI:10.1016/j.nonrwa.2022.103830

D. Liu, H. Wang, and W. Jiang, “Dynamics of a diffusion-advection Lotka-Volterra competition model with stage structure in a spatially heterogeneous environment,” Journal of Differential Equations, vol. 372, pp. 536–563, 2023. DOI:10.1016/j.jde.2023.07.004

L. K. Beay and M. Saija, “A stage-structure Rosenzweig-MacArthur model with effect of prey refuge,” Jambura Journal of Biomathematics, vol. 1, no. 1, pp. 49–64, 2020. DOI:10.34312/jjbm.v1i1.6891

L. K. Beay, A. Suryanto, I. Darti, and Trisilowati, “Hopf bifurcation and stability analysis of the Rosenzweig-MacArthur predator-prey model with stage-structure in prey,” Mathematical Biosciences and Engineering, vol. 17, no. 4, pp. 40804097, 2020.


M. Moustafa, M. H. Mohd, A. I. Ismail, and F. A. Abdullah, “Stage structure and refuge effects in the dynamical analysis of a fractional order Rosenzweig-MacArthur prey-predator model,” Progress in Fractional Differentiation and Applications, vol. 5, no. 1, pp. 49–64, 2019.


Y. Lin, X. Xie, F. Chen, and T. Li, “Convergences of a stage-structured predator-prey model with modified Leslie-Gower and Holling-type II schemes,” Advances in Continuous and Discrete Models, vol. 2016, no. 1, pp. 1–19, 2016. DOI:10.1186/s13662-016-0887-2

R. A. Pratiwi, A. Suryanto, and Trisilowati, “Numerical simulation of Leslie-Gower predator-prey model with stage-structure on predator,” The Journal of Experimental Life Sciences, vol. 8, no. 3, pp. 202–206, 2018. DOI:10.21776/ub.jels.2018.008.03.011

L. K. Beay and M. Saija, “Dynamics of a stage-structure Leslie-Gower model with Michaelis-Menten type harvesting.” AIP Conference Proceedings, vol. 2498, no. 1, p. 020003, 2022. DOI:10.1063/5.0082672

X.-Y. Meng, H.-F. Huo, and X.-B. Zhang, “Stability and global Hopf bifurcation in a Leslie-Gower predator-prey model with stage structure for prey,” Journal of Applied Mathematics and Computing, vol. 60, no. 1–2, pp. 1–25, 2019. DOI:10.1007/s12190-018-1201-0

U. Salamah, A. Suryanto, and W. M. Kusumawinahyu, “Leslie-Gower predator-prey model with stage-structure, Beddington-DeAngelis functional response, and anti-predator behavior.” AIP Conf. Proc., vol. 60, no. 1–2, pp. 020001, 2019. DOI:10.1063/1.5094265

X.-Y. Song and L.-S. Chen, “Optimal harvesting and stability for a predator-prey system with stage structure,” Acta Mathematicae Applicatae Sinica, vol. 18, no. 3, pp. 423430, 2022. DOI:10.1007/s102550200042

R. A. Pratama, S. Toaha, and Kasbawati, “Optimal harvesting and stability of predator prey model with Monod-Haldane predation response function and stage structure for predator.” IOP Conference Series: Earth and Environmental Science, vol. 279, no. 1, p. 012015,


T. Li, X. Huang, and X. Xie, “Stability of a stage-structured predator-prey model with Allee effect and harvesting,” Communications in Mathematical Biology and Neuroscience, vol. 2019, pp. 1–20, 2019. DOI:10.28919/cmbn/3724

H. Li and X. Cheng, “Dynamics of stage-structured predator-prey model with Beddington-DeAngelis functional response and harvesting,” Mathematics, vol. 9, no. 17, p. 2169, 2021. DOI:10.3390/math9172169

L. K. Beay and M. Saija, “Dynamics of a stage-structure Rosenzweig-MacArthur model with linear harvesting in prey and cannibalism in predator,” Jambura Journal of Biomathematics, vol. 2, no. 1, pp. 42–50, 2021. DOI:10.34312/jjbm.v2i1.10470

N. Yaacob and F. Mustapha, “Stability analysis of predator-prey model with stage-structured and the effect of harvesting,” Annals of Mathematical Modeling, vol. 2, no. 1, pp. 7–15, 2022. DOI:10.33292/amm.v2i1.14

J. Al-omari, G. Gumah, and S. Al-Omari, “Dynamics of a harvested stage-structured predator-prey model with distributed maturation delay,” Mathematical Methods in the Applied Sciences, vol. 45, no. 2, pp. 761–769, 2022. DOI:10.1002/mma.7810

A. A. Majeed, “The dynamics and analysis of stage-structured predator-prey model with prey refuge and harvesting involving disease in prey population,” Communications in Mathematics and Applications, vol. 10, no. 3, pp. 337–359, 2019. DOI:10.26713/cma.v10i3.1031

N. Babakordi and H. R. Z. Zangeneh, “Multiple bifurcations analysis in a delayed predator-prey system with disease in prey and stage structure for predator,” International Journal of Dynamics and Control, vol. 8, no. 2, pp. 370–385, 2020. DOI:10.1007/s40435-019-00576-z

E. M. Kafi and A. A. Majeed, “The dynamics and analysis of stage-structured predator-prey model involving disease and refuge in prey population.” Journal of Physics: Conference Series, vol. 1530, no. 1, p. 012036, 2020. DOI:10.1088/1742-6596/1530/1/012036

N. M. S. Sundari and M. Valliathal, “Local stability analysis of epidemiological stage structured predator-prey model with Michaelis Menten predation and prey refuge,” IOSR Journal of Mathematics, vol. 17, no. 3, pp. 1–11, 2021. DOI:10.9790/5728-1703020111

P. Kalra and M. Kaur, “Stability analysis of an eco-epidemiological SIN model with impulsive control strategyfor integrated pest management considering stage-structure in predator,” International Journal of Mathematical Modelling and Numerical Optimisation, vol. 12,

no. 1, pp. 43–68, 2022. DOI:10.1504/IJMMNO.2022.119779

C. J. Heij, C. F. E. Rompas, and C. W. Moeliker, “The biology of the Moluccan megapode Eulipoa wallacei (Aves, Galliformes, Megapodiidae) on Haruku and other Moluccan islands. Part 2. Final Report,” Deinsea, vol. 3, no. 1, pp. 1–126, 1997.

C. F. H. Center, Feline Leukemia Virus. "Supporting Cat Health with Information and Health Studies," https://www.vet.cornell.edu/departments-centers-and-institutes/cornell-feline-health-center/health-information/feline-health-topics/feline-leukemia-virus, Accessed on May 2016.

Y. Medyawati and M. Rahayu, “Analisis Perlindungan Hukum Terhadap Hewan Liar Yang Teraniaya dan Diperjualbelikan (Studi Kasus: Perdagangan Daging Kucing dan Anjing Di Pasar Tomohon Sulawesi Utara),” Jurnal Hukum Adigama, vol. 4, no. 2, 2021.

A. Lahay, M. R. F. Payu, S. L. Mahmud, H. S. Panigoro, and P. Zakaria, “Dynamics of a predator-prey model incorporating infectious disease and quarantine on prey,” Jambura Journal of Biomathematics (JJBM), vol. 3, no. 2, pp. 75–81, 2022. DOI:10.34312/jjbm.v3i2.17162

R. Resmawan, L. Yahya, R. S. Pakaya, H. S. Panigoro, and A. R. Nuha, “Analisis Dinamik Model Penyebaran COVID-19 dengan Vaksinasi,” Jambura Journal of Biomathematics (JJBM), vol. 3, no. 1, 2022. DOI:10.34312/jjbm.v3i1.13176

DOI: https://doi.org/10.37905/jjbm.v4i2.22047

Copyright (c) 2023 Lazarus Kalvein Beay, Zeth Arthur Leleury, Monalisa E. Rijoly, Yopi Andry Lesnussa, Abraham Zacaria Wattimena, Dorteus Lodewyik Rahakbauw

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