Skip Navigation Links
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Impact of Predator Switching in the Disease Outbreak of an Eco-Epidemiological System

Journal of Applied Nonlinear Dynamics 11(1) (2022) 17--32 | DOI:10.5890/JAND.2022.03.002

Aktar Saikh, Nurul Huda Gazi

Department of Mathematics and Statistics, Aliah University, IIA/27, New Town, Kolkata-700160, India

Download Full Text PDF



We introduce an ecological improvement of an eco-epidemiological model by improving the predation principles through predator switching between susceptible and infected prey. The model is analyzed for stability around the uninfected and coexisting equilibria to evaluate the thresholds that control the extinction and coexistence of the species. Next, we investigate the improved model to interpret the effect of changing the functional responses through predator switching. Applying the Arzel\`{a}-Ascoli theorem, we analyze the dynamics of the system around the origin. Numerical simulations are performed to validate the analytical findings. Finally, we conclude some eco-epidemiological comments made through mathematical and numerical observations.


  1. [1]  Mena-Lorcat, J. and Hethcote, H. (1992) Dynamic models of infectious diseases as regulators of population sizes, Journal of mathematical biology, 30, 693-716.
  2. [2]  Hethcote, H., Wang, W., Han, L., and Ma, Z. (2004), A predator-prey model with infected prey, Theoretical Population Biology, 66, 259-268.
  3. [3]  Dobson, A. (1988), The population biology of parasite-induced changes in host behavior, The quarterly review of biology, 63, 139-165.
  4. [4]  Anderson, R. and May, R. (1986), The invasion, persistence and spread of infectious diseases within animal and plant communities, Phil. Trans. R. Soc. Lond. B, 314, 533-570.
  5. [5]  Hadeler, K. and Freedman, H. (1989), Predator-prey populations with parasitic infection, Journal of mathematical biology, 27, 609-631.
  6. [6]  Venturino, E. (1995), Epidemics in predator models: disease among the prey, Mathematical Population Dynamics: Analysis of Heterogenity, Theory of Epidemics, 1, 381-393.
  7. [7]  Chattopadhyay, J. and Arino, O. (1999), A predator-prey model with disease in the prey, Nonlinear Analysis: Theory, Methods $\&$ Applications, 36, 747-766.
  8. [8]  Haque, M. and Chattopadhyay, J. (2007), Role of transmissible disease in an infected prey-dependent predator-prey system, Mathematical and Computer Modelling of Dynamical Systems, 13, 163-178.
  9. [9]  Saikh, A. and Gazi, N. (2017), Mathematical analysis of a predator-prey eco-epidemiological system under the reproduction of infected prey, Journal of Applied Mathematics and Computing, 58, 621-646.
  10. [10]  Han, L., Ma, Z., and Hethcote, H. (2001), Four predator prey models with infectious diseases, Mathematical and Computer Modelling, 34, 849-858.
  11. [11]  Venturino, E. (2002), Epidemics in predator-prey models: disease in the predators, Mathematical Medicine and Biology, 19, 185-205.
  12. [12]  Hilker, F.M. and Malchow, H. (2006) Strange periodic attractors in a prey-predator system with infected prey, Mathematical Population Studies, 13, 119-134.
  13. [13]  Temple, S. (1987), Do predators always capture substandard individuals disproportionately from prey populations? Ecology, 68, 669-674.
  14. [14]  Moore, J. (2002), Parasites and the behavior of animals. Oxford University Press on Demand.
  15. [15]  Peterson, R. and Page, R.E. (1988), The rise and fall of isle royale wolves, 1975-1986, Journal of Mammalogy, 69, 89-99.
  16. [16]  Khan, Q., Balakrishnan, E., and Wake, G. (2004), Analysis of a predator-prey system with predator switching, Bulletin of Mathematical Biology, 66, 109-123.
  17. [17]  Holling, C. (1961), Principles of insect predation, Annual review of entomology, 6, 163-182.
  18. [18]  Takahashi, F. (1964), Reproduction curve with two equilibrium points: A consideration on the fluctuation of insect population, Researches on Population Ecology, 6, 28-36.
  19. [19]  May, R. (1974), Some mathematical problems in biology, providence, ri, Am. Math. Soc, vol. 4, pp. 11-29.
  20. [20]  Murdoch, W. and Oaten, A. (1975), Predation and population stability, Advances in Ecological Research, vol. 9, pp. 1-131, Elsevier.
  21. [21]  Roughgarden, J. and Feldman, M. (1975), Species packing and predation pressure, Ecology, 56, 489-492.
  22. [22]  Tansky, M. (1976), Structure, stability, and efficiency of ecosystem, Progress in theoretical biology, 4, 205-262.
  23. [23]  Tansky, M. (1978), Switching effect in prey-predator system, Journal of Theoretical Biology, 70, 263-271.
  24. [24]  Holgate, P., et al. (1987) A prey-predator model with switching effect, Journal of Theoretical Biology, 125, 61-66.
  25. [25]  Teramoto, E., Kawasaki, K., and Shigesada, N. (1979), Switching effect of predation on competitive prey species, Journal of Theoretical Biology, 79, 303-315.
  26. [26]  Murdoch, W. (1969), Switching in general predators: experiments on predator specificity and stability of prey populations, Ecological monographs, 39, 335-354.
  27. [27]  Freedman, H. and Wolkowicz, G. (1986), Predator-prey systems with group defence: the paradox of enrichment revisited, Bulletin of Mathematical Biology, 48, 493-508.
  28. [28]  Ruan, S. and Freedman, H. (1991), Persistence in three-species food chain models with group defense, Mathematical biosciences, 107, 111-125.
  29. [29]  Freedman, H. and Ruan, S. (1992), Hopf bifurcation in three-species food chain models with group defense, Mathematical biosciences, 111, 73-87.
  30. [30]  Malchow, H., Hilker, F., Sarkar, R., and Brauer, K. (2005) Spatiotemporal patterns in an excitable plankton system with lysogenic viral infection, Mathematical and computer modelling, 42, 1035-1048.
  31. [31]  Birkhoff, G. and Rota, G. (1989), Ordinary differential equations. Wiley, 4th edn.
  32. [32]  La Salle, J. and Lefschetz, S. (1961), Stability by Liapunov's Direct Method with Applications. Mathematics in Science and Engineering 4, Elsevier, Academic Press.