Impacts of Incubation Delay on the Dynamics of an Eco-Epidemiological System—A Theoretical Study

  • N. BairagiEmail author
  • R. R. Sarkar
  • J. Chattopadhyay
Original Article


Parasite and predator play significant role in trophic interaction, productivity and stability of an ecosystem. In this paper, we have studied a host-parasite-predator interaction that incorporates incubation delay. How the qualitative and quantitative behaviors of the system alter with the incubation delay have been discussed both from mathematical and biological point of views. It is observed that for a lower infection rate, the system is stable for all delays; but for a higher infection rate, there exists a threshold value of the delay above which the system is unstable and below which the system is stable leading to the persistence of all the species. Also, the instability arising from the incubation delay may be controlled if somehow the growth rate of predator population is increased. Numerical studies have also been performed to illustrate different analytical findings.


Susceptible population Infected population Predator Linear mass action Holling type II Delay Local stability Hopf-bifurcation 


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Copyright information

© Society for Mathematical Biology 2008

Authors and Affiliations

  1. 1.Centre for Mathematical Biology and Ecology, Department of MathematicsJadavpur UniversityKolkataIndia
  2. 2.Centre for Cellular and Molecular Biology500 007India
  3. 3.Agricultural and Ecological Research UnitIndian Statistical InstituteKolkataIndia

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