Cannibalistic Predator–Prey Model with Disease in Predator — A Delay Model

Abstract

In this paper, we propose and analyze a cannibalistic predator-prey model with a transmissible disease in the predator population. The disease can be transmitted through contacts with infected individuals as well as the cannibalism of an infected predator. We also consider incubation delay in disease transmission, where the incubation period represents the time in which the infectious agent develops in the host. Local stability analysis of the system around the biologically feasible equilibria is studied. Bifurcation analysis of the system around interior equilibrium is also studied. Applying the normal form theory and central manifold theorem, the direction of Hopf bifurcation, the stability and the period of bifurcating periodic solutions are derived. Under appropriate conditions, the permanence of the system with time delay is proved. Our results suggest that incubation delay destabilizes the system and can produce chaos. We also observe that cannibalism can control disease and population oscillations. Extensive numerical simulations are performed to support our analytical results.

Analisis Dinamik Model Predator-Prey dengan Faktor Kanibalisme Pada Predator

“…Salah satu persamaan dalam bidang matematika yaitu persamaan diferensial [2], yang terdiri dari persamaan diferensial linier [3] dan non-linier [4]. Penelitian sebelumnya telah menganalisis model predator-prey antara lain kanibalisme prey yang dapat mengubah dinamika model predator-prey tipe Holling-Tanner [5], efek kanibalisme secara eksplisit pada model predator-prey yang terstruktur oleh tiga usia dalam satu spesies [6], model predator-prey dengan kanibalisme dan adanya penyakit di kedua populasi [7], serta model predator-prey dengan kanibalisme dengan adanya penundaan [8].…”

Dynamical analysis of a juvenile-adult model

“…Mathematical modelling and the pertaining dynamic study have declared that it has significant gradually changing and environmental concepts [5,6,7] for one kind. As intra-specific predation is contain in interproper haunt-haunter models, the intra-specific predation can be one of two obvious illustrated with level-formed prey or predator populations [7,8,9] , or unobvious engaged in prey or hunter populations outside level of form [10,11] . Intra-specific predation was long considerеd and deviant's behavior.…”

Dynamical Study of an Eco-Epidemiological Delay Model for Plankton System with Toxicity

“…A good number of reviews are available on prey–predator dynamics with disease and infection and also their possible ecological and biological impact specified in Biswas et al ( 2010 ), Saifuddin et al ( 2016 ) and Zhao and Jiang ( 2014 ). Upadhyay et al.…”