A delayed eco-epidemiological system with infected prey and predator subject to the weak Allee effect.
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.
Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700108, India. Electronic address: Santanubiswas1988@gmail.com.
Santanu
S
Biswas
Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700108, India. Electronic address: sourav.sasmal@gmail.com.
Sourav Kumar
SK
Sasmal
Department of Biomathematics and Game Theory, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland. Electronic address: samanta.sudip.09@gmail.com.
Sudip
S
Samanta
Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700108, India. Electronic address: safu.vicecaptain@gmail.com.
Md
M
Saifuddin
Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36, Al-Khod 123, Muscat, Oman. Electronic address: qjalil@squ.edu.om.
Qamar Jalil Ahmed
QJ
Khan
Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700108, India. Electronic address: joydev@isical.ac.in.
Joydev
J
Chattopadhyay
D000818:Animals; D003141:Communicable Diseases / Q000635:transmission*; D020387:Food Chain; D008962:Models, Theoretical; D011157:Population Dynamics
Allee effect; Chaos; Eco-epidemiology; Hopf-bifurcation; Time delay