Dynamics of an Eco-Epidemiological Model Consisting of Herding Prey and Harvested Predator


  • Arkan N. Mustafa Department of Mathematics, College of Education, University of Sulaimani, Kurdistan Region, Iraq. Author




Prey -predator model, Herding prey, Functional responses, Stability analysis


In this paper, the dynamics of predator-prey interaction, only at the outer surface of herd formed by prey population and spreading SI-disease in predator population, is modeled mathematically. The boundedness and persistence of our model are studied and local dynamical behaviors are investigated. Furthermore, the conditions that guarantee the occurring of Hopf-bifurcation of the model are established. Finally, we confirm our analytical findings with the help of numerical simulation.


V. Ajraldi, M. Pittavino, E. Venturino,”Modeling behavior in population system”, NonLinear Anal. Real Word Apple., Vol. 12, pp. 2319-2338, (2011). DOI: https://doi.org/10.1016/j.nonrwa.2011.02.002

A. P. Braza, “Predator-Prey dynamics with square root functional responses”, Nonlinear Anal.,Real Word Apple., Vol. 13, pp.1837-1843, (2012). DOI: https://doi.org/10.1016/j.nonrwa.2011.12.014

C.S. Holling, “The components of predation as revealed by a study of small mammal predation of the European pine sawfly", Can. Entomol, Vol. 91, pp. 293-320, (1959a). DOI: https://doi.org/10.4039/Ent91293-5

C.S. Holling, “Some characteristics of simple types of predation and parasitism”, Can. Entomol., Vol. 91, pp. 385-395, (1959b). DOI: https://doi.org/10.4039/Ent91385-7

C.S. Holling,, ”Functional response of invertebrate predator to prey density”, Mem. Entomol. Soc. Can., Vol. 45, pp. 3-60, (1965).

A. Lotka, “Elements of Physical Biology”, William and Wilkins, Baltimore,MD, (1925).

T. K. Kar,“Modelling and analysis of a harvested prey–predator system incorporating a prey Refuge”, Journal of Computational and Applied Mathematics. Vol. 185, pp.19 - 33, (2006). DOI: https://doi.org/10.1016/j.cam.2005.01.035

R.K. Naji, A. N. Mustafa, “The Dynamics of an Eco-Epidemiological Model with Nonlinear Incidence Rate”, J. A. Mathematics , (2012). DOI: https://doi.org/10.1155/2012/852631

M. Rosenzweig and R. MacArthur, “Graphical Representation and Stability Conditions of Predator-Prey Interactions”, American Naturalist. Vol. 97, pp. 209-223, (1963). DOI: https://doi.org/10.1086/282272

V. Votera, “Variazioni e fluttuazioni del numero di numero di individui in specie animal Convivneti”, Mem. Accad. Naz. Lincei, Cl. Sci. Fis.Mat. Nat. Vol. 6,No. 2, pp. 31-113,(1926).

R.K. Naji, A. N. Mustafa, “The dynamics of a three species food web model with disease in intermediate predator”, Journal of zankoy Sulaimani, (2013). DOI: https://doi.org/10.17656/jzs.10246



How to Cite

Dynamics of an Eco-Epidemiological Model Consisting of Herding Prey and Harvested Predator. (2019). Journal of Zankoy Sulaimani - Part A, 21(2), 45-56. https://doi.org/10.17656/jzs.10756