A delayed eco-epidemiological system with infected prey and predator subject to the weak Allee effect

Santanu Biswas, Sourav Kumar Sasmal, Sudip Samanta, Md Saifuddin, Qamar Jalil Ahmed Khan, Joydev Chattopadhyay*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)


We consider a system of delay differential equations to represent predator-prey eco-epidemic dynamics with weak Allee effect in the growth of predator population. The basic aim of the paper is to observe the dynamics of such system under the influence of gestation delay of predator and Allee parameter. We analyze essential mathematical features of the proposed model such as uniform persistence, stability and Hopf-bifurcation at the interior equilibrium point of the system. Global asymptotic stability analysis of the positive equilibrium points by constructing a suitable Lyapunov function for the delayed model is carried out separately. We perform several numerical simulations to illustrate the applicability of the proposed mathematical model and our analytical findings. We observe that the system exhibits chaotic oscillation due to increase of the delay parameter τ. We also observe that there is a threshold of Allee parameter above which the predator population will be washed away from the system.

Original languageEnglish
Pages (from-to)198-208
Number of pages11
JournalMathematical Biosciences
Publication statusPublished - May 1 2015


  • Allee effect
  • Chaos
  • Eco-epidemiology
  • Hopf-bifurcation
  • Time delay

ASJC Scopus subject areas

  • Statistics and Probability
  • Medicine(all)
  • Modelling and Simulation
  • Immunology and Microbiology(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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