Global Stability of Harvested Prey–Predator Model with Infection in Predator Species

  • Nishant Juneja
  • Kulbhushan Agnihotri
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 701)


In the present work, a model on predator–prey system in which only the predator population is infected by a disease is proposed and analyzed. It is considered that both the prey and predator species are harvested at different harvesting rates and differential predation rates for susceptible, and infected predators are also taken. Conditions for the existence and stability of all feasible equilibrium points are obtained. It is observed that nonzero equilibrium point is always globally stable whenever it is locally stable. It has been noticed that the reduced predation rate of infected predator and controlled harvesting of predator species is helpful in controlling the spread of disease.


Carrying capacity Harvesting Predator Prey Predation rate 



The first author Nishant Juneja, being a research scholar at I.K.G. Punjab Technical University, Kapurthala highly acknowledges this university for its valuable inputs on present research.


  1. 1.
    Anderson, R.M., May, R.M.: The invasion, persistence and spread of infectious diseases in animal and plant communities. Philos. Trans. R. Soc. Lond. B Biol. Sci. 314, 533–570 (1982)Google Scholar
  2. 2.
    Anderson, R.M., May, R.M.: The population dynamics of micro-parasite and their invertebrate hosts. Philos. Trans. R. Soc. Lond. B Biol. Sci. 291, 451–524 (1982)CrossRefGoogle Scholar
  3. 3.
    Hadeler, K.P., Freedman, H.I.: Predator-prey populations with parasitic infection. J. Math. Biol. 27, 609–631 (1989)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Chattopadhay, J., Arino, O.: A predator-prey model with disease in the prey. Nonlinear Anal. 36, 747–766 (1999)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Chattopadhay, J., Arino, O., Bairagi, N.: Pelicans at risk in Salton sea—an eco-epidemiological study. Ecol. Model. 136, 103–112 (1999)CrossRefGoogle Scholar
  6. 6.
    Greenhalgh, D., Haque, M.: A predator-prey model with the disease in prey species only. Math. Methods Appl. Sci. 30, 911–929 (2006)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Lenbury, Y., Rattanmongkonkul, S., Tumrasvin, N., Amornsamankul, S.: Predator-prey interaction coupled by parasitic infection: limit cycles and chaotic behavior. Math. Comput. Model. 30, 131–146 (1999)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Agnihotri, K., Juneja, N.: An eco-epidemic model with disease in both prey and predator. IJAEEE 4(3), 50–54 (2015)Google Scholar
  9. 9.
    Agnihotri, K., Juneja, N.: Predator-prey system with infection in predator only. Elixir Appl. Math. 83, 32909–32917 (2015)Google Scholar
  10. 10.
    Chattopadhay, J., Bairagi, N., Chaudhuri, S.: Harvesting as a disease control measure in an eco-epidemiological system—a theoretical study. Math. Biosci. 217(2), 134–144 (2009)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Kar, T.K., Ghorai, A.: Dynamic behavior of a delayed predator-prey model with harvesting. Appl. Math. Comput. 217, 9085–9104 (2011)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Guria, S.: Effect of harvesting and infection on predator in a prey-predator system. Nonlinear Dyn. 81, 917–930 (2015)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Wang, X., Liu, H., Xu, C.: Hopf bifurcations in a predator-prey system of population allelopathy with a discrete delay and a distributed delay. Nonlinear Dyn. 69(4), 2155–2167 (2012)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Lenzini, P., Rebaza, J.: Non-constant predator harvesting on ratio-dependent predator-prey models. Appl. Math. Sci. 4(16), 791–803 (2016)zbMATHGoogle Scholar
  15. 15.
    Gupta, R.P., Banerjee, M., Chandra, P.: Bifurcation analysis and control of Leslie-Gower Predator–Prey model with Michaelis-Menten type prey-harvesting. Differ. Equ. Dyn. Syst. 20, 339–366 (2016)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Gulland, F.: The impact of infectious diseases on wild animal populations: a review. Ecol. Infect. Dis. Nat. Popul. 1, 20–51 (1995)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.I. K. Gujral Punjab Technical UniversityKapurthalaIndia
  2. 2.Shaheed Bhagat Singh State Technical CampusFerozepurIndia

Personalised recommendations