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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Dynamical Analysis of an Eco-epidemic System with Different Forms of Prey Refuges and Predator Harvesting

Discontinuity, Nonlinearity, and Complexity 13(1) (2024) 95--112 | DOI:10.5890/DNC.2024.03.008

Md Sarijul Islam, Sajjad Hossain, Sahabuddin Sarwardi

Department of Mathematics and Statistics, Aliah University IIA/27, New Town, Kolkata - 700 160, India

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Abstract

The present article deals with an eco-epidemiological model consisting of one prey and two predator population subjected to predator infection and predator harvesting. It has been considered two different types of functional response incorporating linear type refuge for susceptible predator and non-linear type refuge for infected predator. After formulating the model system, the positivity and boundedness of the solution, the persistence of the proposed system have been discussed. Along with the existence and stability of the biologically feasible equilibrium points, different types of bifurcation have been thoroughly investigated and in this regard, some suitable graphical representations are executed. Some numerical results are performed to support our analytical findings.

References

  1. [1]  Malthus, T.R. (1798), An Essay on the Principle of Population, J. Johnson in St. Paul's Churchyard, London.
  2. [2]  Lotka, A.J. (1956), Elements of Mathematical Biology, Dover: New York.
  3. [3]  Volterra, V. and D'Ancona U. (1931), La concorrenza vitale tra le specie dell'ambiente marino, Vlle Congr. Int. acquicult et de p\^{e}che, Paris, 1-14.
  4. [4]  Zhou, Y., Sun, W., Song, Y., Zheng, Z., Lu, J. and Chen, S. (2019), Hopf bifurcation analysis of a predator-prey model with Holling-II type functional response and a prey refuge, Nonlinear Dynamics, 97(2), 1439-1450.
  5. [5]  Haque, M.M. and Sarwardi, S. (2020), Complex dynamics of an exploited prey-predatormodel with nonlinear prey refuge, Discontinuity, Nonlinearity, and Complexity, 9(1), 99-116.
  6. [6]  Hassell, M.P. (2020), The dynamics of arthopod predator-prey systems, Princeton University Press.
  7. [7]  González-Olivares, E. and Ramos-Jiliberto, R. (2003), Dynamic consequences of prey refuges in a simple model system: more prey, fewer predators and enhanced stability, Ecological Modelling, 166(1-2), 135-146.
  8. [8]  McNair, J.N. (1986), The effects of refuges on predator-prey interactions: a reconsideration, Theoretical Population Biology, 29(1), 38-63.
  9. [9]  Das, H., Shaikh, A.A., and Sarwardi, S. (2020), Mathematical analysis of an eco-epidemic model with different functional responses of healthy and infected predators on prey species, Journal of Applied Nonlinear Dynamics, 9(4), 667-684.
  10. [10]  Tripathi, J.P., Bugalia, S., Choudhary, H., Kumar, D., and Singh, J. (2021), Role of harvesting and Allee in a predator-prey model with disease in the both populations, Nonlinear Studies, 28(4).
  11. [11]  Huang, J., Gong, Y., and Ruan, S. (2013), Bifurcation analysis in a predator-prey model with constant-yield predator harvesting, Discrete and Continuous Dynamical Systems, 18(8), 2101.
  12. [12]  Jana, S., Chakraborty, M., Chakraborty, K., and Kar, T.K. (2012), Global stability and bifurcation of time delayed prey predator system incorporating prey refuge, Mathematics and Computers in Simulation, 85, 57-77.
  13. [13]  Sarif, N. and Sarwardi, S. (2021), Analysis of Bogdanov-Takens bifurcation of codimension two in a Gause-Type model with constant harvesting of both species and delay effect, Journal of Biological Systems, 29(3), 741-771.
  14. [14]  Yuan, R., Wang, Z., and Jiang, W. (2016), Global Hopf bifurcation of a delayed diffusive predator-prey model with Michaelis-Menten-type prey harvesting, Applicable Analysis, 95(2), 444-466.
  15. [15]  Mandal, U.K., Sharma, K.L., Venkanna, K., Korwar, G.R., Reddy, K.S., Reddy, N.N., Venkatesh, G., Masane, R.N., and Yadaiah, P. (2015), Evaluating hydrogel application on soil water availability and crop productivity in semiarid tropical red soil, Indian Journal of Dryland Agricultural Research and Development, 30(2), 1-10.
  16. [16]  Anderson, R.M. and May, R.M. (1981), The population dynamics of microparasites and their invertebrate hosts, Philosophical Transactions of the Royal Society of London. B, Biological Sciences, 291(1054), 451-524.
  17. [17]  Haque, M. (2010), A predator-prey model with disease in the predator species only, Nonlinear Analysis: Real World Applications, 11(4), 2224-2236.
  18. [18]  Rahman, M.S. and Chakravarty, S. (2013), A predator-prey model with disease in prey, Nonlinear Analysis: Modelling and Control, 18(2), 191-209.
  19. [19]  Mondal, A., Pal, A.K., and Samanta, G.P. (2019), On the dynamics of evolutionary Leslie-Gower predator-prey eco-epidemiological model with disease in predator, Ecological Genetics and Genomics, 10, 100034.
  20. [20]  Saha, S. and Samanta, G.P. (2019), Analysis of a predator-prey model with herd behavior and disease in prey incorporating prey refuge, International Journal of Biomathematics, 12(01), 1950007.
  21. [21]  Saha, S., Maiti, A., and Samanta, G.P. (2018), A Michaelis-Menten predator-prey model with strong Allee effect and disease in prey incorporating prey refuge, International Journal of Bifurcation and Chaos, 28(06), 1850073.
  22. [22]  Mandal, P. and Farag$\acute{\text{o}}$, I. (2021), Operator splitting and error analysis in malaria modeling, Applied Mathematics and Computation, 410, 126446.
  23. [23]  Wang, S., Ma, Z., and Wang, W. (2018), Dynamical behavior of a generalized eco-epidemiological system with prey refuge, Advances in Difference Equations, 2018(1), 1-20.
  24. [24]  Haque, M. (2009), Ratio-dependent predator-prey models of interacting populations, Bulletin of Mathematical Biology, 71(2), 430-452.
  25. [25]  Haque, M., Sarwardi, S., Preston, S., and Venturino, E. (2011), Effect of delay in a Lotka-Volterra type predator-prey model with a transmissible disease in the predator species, Mathematical Biosciences, 234(1), 47-57.
  26. [26]  Haque, M., Rahman, M.S., and Venturino, E. (2013), Comparing functional responses in predator-infected eco-epidemics models, BioSystems, 114(2), 98-117.
  27. [27]  Venturino, E. (2002), Epidemics in predator-prey models: disease in the predators, Mathematical Medicine and Biology, 19(3), 185-205.
  28. [28]  Sieber, M., Malchow, H., and Hilker, F.M. (2014), Disease-induced modification of prey competition in eco-epidemiological models, Ecological Complexity, 18, 74-82.
  29. [29]  Jana, S., Guria, S., Das, U., Kar, T.K., and Ghorai, A. (2015), Effect of harvesting and infection on predator in a prey-predator system, Nonlinear Dynamics, 81(1), 917-930.
  30. [30]  Melese, D., Muhye, O. and Sahu, S.K. (2020), Dynamical behavior of an eco-epidemiological model incorporating prey refuge and prey harvesting, Applications and Applied Mathematics, 15(2), 28.
  31. [31]  Kumar, U., Mandal, P.S., and Venturino, E. (2020), Impact of Allee effect on an eco-epidemiological system, Ecological Complexity, 42, 100828.
  32. [32]  Saikh, A. and Gazi, N.H. (2020), A mathematical study of a two species eco-epidemiological model with different predation principles, Discontinuity, Nonlinearity, and Complexity, 9(2), 309-325.
  33. [33]  Hale, J. (1977), Theory of Functional Differential Equations, Springer-Verlag, New York, Heidelberg, Berlin.
  34. [34]  Birkhoff, G. and Rota, C. (1982), Ordinary differential equations, John Wiley and Sons, New York.
  35. [35]  Gard, T.C. and Hallam, T.G. (1979), Persistence in food webs I Lotka-Volterra food chains, Bulletin of Mathematical Biology, 41(6), 877-891.
  36. [36]  Hale, J. (1989), Ordinary differential equation, Klieger Publishing Company, Malabar.
  37. [37]  Wiggins, S., Wiggins, S., and Golubitsky, M. (1990), Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2, New York: Springer-Verlag.
  38. [38]  Sotomayor, J. (1973), Generic Bifurcations of Dynamical Systems: Dynamical Systems, Academic Press, 561-582.
  39. [39]  Shaikh, A.A., Das, H., and Sarwardi, S. (2020), Dynamics of an eco-epidemiological system with disease in competitive prey species, Journal of Applied Mathematics and Computing, 62(1), 525-545.
  40. [40]  Mbava, W., Mugisha, J.Y.T., and Gonsalves, J.W. (2017), Prey, predator and super-predator model with disease in the super-predator, Applied Mathematics and Computation, 297, 92-114.
  41. [41]  Baishya, C., Achar, S.J., Veeresha, P., and Prakasha, D.G. (2021), Dynamics of a fractional epidemiological model with disease infection in both the populations, Chaos: An Interdisciplinary Journal of Nonlinear Science, 31(4), 043130.
  42. [42]  Liu, X. and Wang, C. (2010), Bifurcation of a predator-prey model with disease in the prey, Nonlinear Dynamics, 62(4), 841-850.
  43. [43]  Rashkov, P., Venturino, E., Aguiar, M., Stollenwerk, N., and Kooi, B.W. (2019), On the role of vector modeling in a minimalistic epidemic model, Mathematical Biosciences and Engineering, 16(5), 4314-4338.
  44. [44]  Meng, X.Y., Qin, N.N., and Huo, H.F. (2018), Dynamics analysis of a predator-prey system with harvesting prey and disease in prey species, Journal of Biological Dynamics, 12(1), 342-374.
  45. [45]  Haque, M. and Sarwardi, S. (2016), Effect of toxicity on a harvested fishery model, Modeling Earth Systems and Environment, 2(3), 1-10.
  46. [46]  Thota, S. (2020), A mathematical study on a diseased prey-predator model with predator harvesting, Asian Journal of Fuzzy and Applied Mathematics, 8(2), 16-21.
  47. [47]  Amalia, R.D. and Arif, D.K. (2018), Optimal control of predator-prey mathematical model with infection and harvesting on prey, In Journal of Physics: Conference Series (IOP Publishing), 974(1), 012050.

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