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

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

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
Volume263
DOIs
Publication statusPublished - May 1 2015

Fingerprint

Allee Effect
Population Growth
Predator
Prey
Theoretical Models
predators
Pregnancy
Hopf bifurcation
Chaotic systems
Lyapunov functions
Asymptotic stability
Population
Differential equations
Equilibrium Point
Mathematical models
Uniform Persistence
Computer simulation
Predator-prey
Global Asymptotic Stability
oscillation

Keywords

  • 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

Cite this

A delayed eco-epidemiological system with infected prey and predator subject to the weak Allee effect. / Biswas, Santanu; Sasmal, Sourav Kumar; Samanta, Sudip; Saifuddin, Md; Khan, Qamar Jalil Ahmed; Chattopadhyay, Joydev.

In: Mathematical Biosciences, Vol. 263, 01.05.2015, p. 198-208.

Research output: Contribution to journalArticle

Biswas, Santanu ; Sasmal, Sourav Kumar ; Samanta, Sudip ; Saifuddin, Md ; Khan, Qamar Jalil Ahmed ; Chattopadhyay, Joydev. / A delayed eco-epidemiological system with infected prey and predator subject to the weak Allee effect. In: Mathematical Biosciences. 2015 ; Vol. 263. pp. 198-208.
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