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Prey, predator and super-predator model with disease in the super-predator

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  • Mbava, W.
  • Mugisha, J.Y.T.
  • Gonsalves, J.W.

Abstract

The dynamics of a predator–prey model with disease in super-predator are investigated. The predator is under immense competition from the super-predator and is also facing extinction. The disease is considered as biological control to allow the predator population to regain from a low number. The results highlight that in the absence of additional mortality on predator by super-predator, the predator population survives extinction. At current levels of disease incidence, the super-predator population is wiped out by the disease. However, the super-predator population survives extinction if the disease incidence rate is low. Persistence of all populations is possible in the case of low disease incidence rate and no additional mortality imparted on predator. Furthermore, a two-species subsystem, prey and predator, is considered as a special case to determine the effect of super-predator removal from the system, on the survival of the predator. This is treated as a contrasting case of the smaller parks. The results show that the predator population thrives well in the total absence of its main competitor, with its population rising to at least twice the initial value.

Suggested Citation

  • Mbava, W. & Mugisha, J.Y.T. & Gonsalves, J.W., 2017. "Prey, predator and super-predator model with disease in the super-predator," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 92-114.
    • Handle: RePEc:eee:apmaco:v:297:y:2017:i:c:p:92-114
    DOI: 10.1016/j.amc.2016.10.034
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    References listed on IDEAS

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    1. Lu, Yang & Li, Dan & Liu, Shengqiang, 2016. "Modeling of hunting strategies of the predators in susceptible and infected prey," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 268-285.
    2. Sahoo, Banshidhar, 2015. "Role of additional food in eco-epidemiological system with disease in the prey," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 61-79.
    3. Chakraborty, Kunal & Das, Kunal & Haldar, Samadyuti & Kar, T.K., 2015. "A mathematical study of an eco-epidemiological system on disease persistence and extinction perspective," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 99-112.
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    Cited by:

    1. Yılmaz, Zeynep & Maden, Selahattin & Gökçe, Aytül, 2022. "Dynamics and stability of two predators–one prey mathematical model with fading memory in one predator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 526-539.
    2. Chakraborty, Bhaskar & Ghorai, Santu & Bairagi, Nandadulal, 2020. "Reaction-diffusion predator-prey-parasite system and spatiotemporal complexity," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    3. Rihan, F.A. & Rajivganthi, C, 2020. "Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    4. Alsakaji, Hebatallah J. & Kundu, Soumen & Rihan, Fathalla A., 2021. "Delay differential model of one-predator two-prey system with Monod-Haldane and holling type II functional responses," Applied Mathematics and Computation, Elsevier, vol. 397(C).

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