Impacts of Fisheries Harvesting on Fish-Bird Model for the Salton Sea Region
DOI:
https://doi.org/10.26713/cma.v15i2.2677Keywords:
Fish-bird model, Harvesting, Local stability analysis, Chaotic attractor, Quasi periodic ascillationAbstract
This study investigates the impact of fisheries harvesting on a Fish-bird model, focusing specifically on the presence of illnesses in fish and the consequential effects on bird populations. Tilapia fish, serving as the primary dietary source for pelican birds in the Salton Sea region, face the risk of overexploitation due to increased fishing activities. The study reveals that heightened harvesting rates can lead to the eventual extinction of bird species over time, highlighting the delicate balance between fishing sustainability and ecological preservation. The equilibrium and stability of the system are analyzed, with numerical simulations illustrating various dynamical behaviors such as chaotic attractors and quasi-periodic oscillations. The harvesting model considers the extraction of both susceptible and infected fish, demonstrating that an increase in the harvesting rate of susceptible fish poses a significant threat to bird populations. Conversely, while maintaining a constant harvesting rate of infected fish, the bird population remains viable even for varying levels of infected harvesting rates. Ultimately, the study underscores the importance of sustainable fishing practices, cautioning against the overexploitation of susceptible fish, which could lead to the extinction of birds in the Salton Sea region.
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References
D. Adak and N. Bairagi, Complexity in a predator-prey-parasite model with nonlinear incidence rate and incubation delay, Chaos, Solitons & Fractals 81 (2015), 271 – 289, DOI: 10.1016/j.chaos.2015.09.028.
M. Banerjee, B. W. Kooi and E. Venturino, An ecoepidemic model with prey herd behavior and predator feeding saturation response on both healthy and diseased prey, Mathematical Modelling of Natural Phenomena 12(2) (2017), 133 – 161, DOI: 10.1051/mmnp/201712208.
B. Barman and B. Ghosh, Role of time delay and harvesting in some predator–prey communities with different functional responses and intra-species competition, International Journal of Modelling and Simulation 42(6) (2022) 883 – 901, DOI: 10.1080/02286203.2021.1983747.
V. Capasso and G. Serio, A generalization of the Kermack-McKendrick deterministic epidemic model, Mathematical Biosciences 42(1-2) (1978), 43 – 61, DOI: 10.1016/0025-5564(78)90006-8.
J. Chattopadhyay and N. Bairagi, Pelicans at risk in Salton sea – an eco-epidemiological model, Ecological Modelling 136 (2-3) (2001), 103 – 112, DOI: 10.1016/S0304-3800(00)00350-1.
J. Chattopadhyay and O. Arino, A predator-prey model with disease in the prey, Nonlinear Analysis: Theory, Methods & Applications 36(6) (1999), 747 – 766, DOI: 10.1016/S0362-546X(98)00126-6.
J. Chattopadhyay, P. D. N. Srinivasu and N. Bairagi, Pelicans at risk in Salton Sea – an ecoepidemiological model-II, Ecological Modelling 167(1-2) (2003), 199 – 211, DOI: 10.1016/S0304-3800(03)00187-X.
D. Greenhalgh, Q. J. A. David and F. A. Al-Kharousi, Eco-epidemiological model with fatal disease in the prey, Nonlinear Analysis: Real World Applications 53 (2020), 103072, DOI: 10.1016/j.nonrwa.2019.103072.
J. K. Hale, Functional differential equations, in: Analytic Theory of Differential Equations, Lecture Notes in Mathematics (LNM, Volume 183), pp. 9 – 22, Springer, Berlin — Heidelberg (1971), DOI: 10.1007/BFb0060406.
W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proceedings of the Royal Society of London – Series A 115(772) (1927), 700 – 721, DOI: 10.1098/rspa.1927.0118.
B. Kumar and R. K. Sinha, Dynamics of an eco-epidemic model with Allee effect in prey and disease in predator, Computational and Mathematical Biophysics 11(1) (2023), 20230108, DOI: 10.1515/cmb-2023-0108.
A. J. Lotka, Elements of Physical Biology, Williams & Wilkins Company, USA, xxx + 460 pages (1925).
A. Mahata, S. P. Mondal, B. Roy and S. Alam, Study of two species prey-predator model in imprecise environment with MSY policy under different harvesting scenario, Environment, Development and Sustainability 23 (2021), 14908 – 14932, DOI: 10.1007/s10668-021-01279-2.
P. Panja, S. Poria and S. K. Mondal, Analysis of a harvested tritrophic food chain model in the presence of additional food for top predator, International Journal of Biomathematics 11(04) (2018), 1850059, DOI: 10.1142/S1793524518500596.
L. Perko, Differential Equations and Dynamical Systems, Vol. 7, Springer Science & Business Media, xiv + 557 pages (2013), DOI: 10.1007/978-1-4613-0003-8.
A. A. Shaikh and H. Das, An eco-epidemic predator–prey model with Allee effect in prey, International Journal of Bifurcation and Chaos 30(13) (2020), 2050194, DOI: 10.1142/S0218127420501941.
R. K. Upadhyay and P. Roy, Spread of a disease and its effect on population dynamics in an eco-epidemiological system, Communications in Nonlinear Science and Numerical Simulation 19(12) (2014), 4170 – 4184, DOI: 10.1016/j.cnsns.2014.04.016.
R. K. Upadhyay, N. Bairagi, K. Kundu and J. Chattopadhyay, Chaos in eco-epidemiological problem of the Salton Sea and its possible control, Applied Mathematics and Computation 196(1) (2008), 392 – 401, DOI: 10.1016/j.amc.2007.06.007.
R. K. Upadhyay, S. Kumari, S. Kumari and V. Rai, Salton sea: An ecosystem in crisis, International Journal of Biomathematics 11(08) (2018), 1850114, DOI: 10.1142/S1793524518501140.
V. Volterra, Variazioni e uttuazioni del numero d’individui in specie animali conviventi, Societá anonima tipografica “Leonardo da Vinci” (1926).
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