On the dynamical behavior of an Eco-Epidemiological model

Document Type : Research Paper

Author

Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

Abstract

The aim of this article is to study the dynamical behavior of an eco-epidemiological model. A prey-predator model comprising infectious disease in prey species and stage structure in predator species is suggested and studied. Presumed that the prey species growing logistically in the absence of predator and the ferocity process happened by Lotka-Volterra functional response. The existence, uniqueness, and boundedness of the solution of the model are investigated. The stability constraints of all equilibrium points are determined. The constraints of persistence of the model are established. The local bifurcation near every equilibrium point is analyzed. The global dynamics of the model are investigated numerically and confronted with the obtained outcomes.

Keywords

[1] D.K. Bahlool, H.A. Satar and H.A. Ibrahim, Order and chaos in a prey-predator model incorporating refuge,
disease, and harvesting, J. Appl. Math. 2020 (2020) ID 5373817, 19 pages.
[2] K. P. Das, A Mathematical Study of a Predator-Prey Dynamics with Disease in Predator, Int. Schol. Res. Not.
2011 (2011) ID 807486.
[3] K.P. Das, K. Kundu and J. Chattopadhyay, A predator-prey mathematical model with both the populations
affected by diseases, Eco. Comp. 8 (2011) 68–80.
[4] K.P. Das, S.K. Sasmal and J. Chattopadhyay, Disease control through harvesting – conclusion drawn from a
mathematical study of a predator-prey model with disease in both the population, Int. J. Biomat. Syst. Bio. 1
(2014) 1–29.
[5] H.I. Freedman and P. Waltman, Persistence in models of three interaction predator-prey populations, Math.
Biosci. 68 (1984) 213–231.
[6] M. Haque, A predator–prey model with disease in the predator species only, Nonlinear Anal. Real World Appl. 11
(2010) 2224–2236.
[7] M.W. Hirsch and S. Smale, Differential Equation, Dynamical System and Linear Algebra, Academic Press, 197).
[8] R.A. Horn and C.R. Johanson, Matrix Analysis, Cambridge University Press, 1985.
[9] Y. Hsieh and C. Hsiao, Predator-prey model with disease infection in both populations, Math. Med. Bio. 25 (2008)
247–266.[10] H.A. Ibrahim and R.K. Naji, A prey-predator model with Michael Mentence type of predator harvesting and
infectious disease in prey, Iraqi J. Sci. 61 (2020) 1146–1163.
[11] S. Kant and V. Kumar, Stability analysis of predator-prey system with migrating prey and disease infection in
both species, Appl. Math. Model. 42 (2017) 509–539.
[12] R.M. May, Stability and Complexity in Model Ecosystems, Princeton, NJ: Princeton University Press, 1973.
[13] R.M. May and R.M. Anderson, Regulation and stability of host-parasite population interactions: I. Regulatory
processes, J. Animal Eco. 47(1978) 219–247.
[14] M.V.R. Murthy and D. K. Bahlool, Modeling and analysis of a prey-predator system with disease in predator,
IOSR J. Math. 12 (2016) 21–40.
[15] R.K. Naji and R.A. Hamodi, The dynamics of an ecological model with infectious disease, Global J. Engin. Sci.
Res. 3 (2016) 69–89.
[16] R. K. Naji and S. J. Majeed, A study of delayed prey-predator model with stage-structure in predator, Global J.
Pure Appl. Math. 13 (2017) 6647-6671.
[17] Md.S. Rahman and S. Chakravarty, A predator-prey model with disease in prey, Nonlinear Anal. Model. Cont.
18 (2013) 191–209.
[18] H.A. Satar, The dynamics of an eco-epidemiological model with allee effect and harvesting in the predator, J.
Southwest Jiaotong Univ. 55(2020).
[19] D. Savitri1 and A. Abadi, Dynamics and numerical simulation of stage structure prey-predator models, Proc. Int.
Conf. Sci. and Tech. 1 (2018).
[20] W. Wang and L. Chen, A predator-prey system with stage-structure for predator, Comput. Math. Appl. 33 (1997)
83–91.
Volume 12, Issue 2
November 2021
Pages 1749-1767
  • Receive Date: 23 March 2021
  • Revise Date: 16 June 2021
  • Accept Date: 01 July 2021