Study of a symbiotic system with disease and delay

Kusumika Kundu*, Sudip Samanta, Pijush Panday, Nikhil Pal, Qamar Khan, Joydev Chattopadhyay

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In the present paper, we study a model with two symbiotic species, where one of the species is subject to disease infection. We observe that for increasing mutualism, the system may become unbounded. We also perform sensitivity analysis to identify the sensitive parameters of the model. Further, we incorporate incubation delay in the disease transmission and investigate how the qualitative behavior of the system changes for the incubation delay. We analyze the model with the help of stability and bifurcation analysis. Taking time-delay as bifurcation parameter, Hopfbifurcation and direction of Hopf-bifurcation are investigated near the coexistence equilibrium point. We illustrate analytical findings through numerical simulations.

Original languageEnglish
Pages (from-to)535-557
Number of pages23
JournalNonlinear Studies
Issue number3
Publication statusPublished - 2018


  • Disease
  • Hopf-bifurcation
  • Sensitivity analysis
  • Symbiosis
  • Time-delay

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics


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