An Eco-Epidemic Predator–Prey Model with Allee Effect in Prey

Abstract

This article describes the dynamics of a predator–prey model with disease in predator population and prey population subject to Allee effect. The positivity and boundedness of the solutions of the system have been determined. The existence of equilibria of the system and the stability of those equilibria are analyzed when Allee effect is present. The main objective of this study is to investigate the impact of Allee effect and it is observed that the system experiences Hopf bifurcation and chaos due to Allee effect. The results obtained from the model may be useful for analyzing the real-world ecological and eco-epidemiological systems.

Dynamical behaviors of stochastic eco‐epidemic predator–prey model with Allee effect in prey and Lévy jump

“…Inspired by the article above, we consider a stochastic predator–prey model with the Allee effect and Lévy jump, in which the Allee effect significantly influences the variation in prey population size and susceptible and infected predators make up two groups of predator population as a result of the disease. In contrast to [9], we change from Holling type II to Beddington–DeAngelis functional response function to describe the predation rate influenced by predators, change the Allee effect form, and add the white and Lévy noise effects. Firstly, we consider the following model without stochastic effects: …”

“…Furthermore, in their paper, it was assumed that the infected predators cannot hunt, whereas the susceptible predators can. The following is the model in [9]:…”

“…As a result, we must develop an appropriate predator–prey model to depict such system and study the dynamic behaviors. For instance, Shaikh and Das studied an eco‐epidemic predator–prey model with Allee effect in [9]. They introduce Allee effect into the prey population and disease with Holling type II incidence rate into the predator population, which separates the predator population into two groups: susceptible predators and infected predators.…”

“…Furthermore, in their paper, it was assumed that the infected predators cannot hunt, whereas the susceptible predators can. The following is the model in [9]: $$$$ \left\{\begin{array}{l}\frac{\mathrm{d}x(t)}{\mathrm{d}t}= Rx\left(1-\frac{x}{K}\right)\left(\frac{x}{L}-1\right)-\frac{A_1 xy}{B_1+x},\\ {}\frac{\mathrm{d}y(t)}{\mathrm{d}t}=\frac{C_1{A}_1 xy}{B_1+x}-\frac{\lambda yz}{B_2+y}-{D}_2y,\\ {}\frac{\mathrm{d}z(t)}{\mathrm{d}t}=\frac{\lambda yz}{B_2+y(t)}-{D}_3z,\end{array}\right. $$$$ where $$$ x(t),y(t) $$$, and $$$ z(t) $$$ are the population density of prey, susceptible predator, and infected predator at time $$$ t $$$, respectively; $$$ K $$$ is the environmental carrying capacity of prey pop...…”

Dynamical Analysis of Two-Preys and One Predator Interaction Model with An Allee Effect on Predator

“…Their debate focuses on the best harvesting policy for the greatest economic gain while ensuring the long-term viability of the population. Absos Ali Shaikh and Harekrishna Das [20] report the dynamics of a prey-predator model with sickness in the predator population and prey population sensitive to the Allee effect. Studying the dynamics of a preypredator model in which both the prey and the predator exhibit herd behavior is the goal of the work of Debasis Manna, Alakes Maiti, and G.P.…”