|
|
 |
| |
|
|
|
A Design of Predictive Eco-Epidemiological Fractional Model (3 Species) Induced by Disease in Prey |
|
|
|
PP: 691-704 |
|
|
doi:10.18576/pfda/110405
|
|
|
|
Author(s) |
|
|
|
Muhammad Shoaib Arif,
Kamaleldin Abodayeh,
Asad Ejaz,
|
|
|
|
Abstract |
|
|
| This study develops a fractional-order eco-epidemiological model to describe the dynamics of a three-species system comprising susceptible prey US(t), infected prey UI(t), and predators V(t). The disease is assumed to spread non-vertically among the prey, governed by a transmission rate γ, and only affects the susceptible prey. The proposed model uses Caputo fractional derivatives to incorporate memory effects, offering a more realistic framework for ecological systems. The existence and uniqueness of the solution are established using the Lipschitz condition. We identify and analyze biologically meaningful equilibrium points, including the infection-free equilibrium and coexistence equilibrium, and investigate their stability within the fractional-order setting. A fractional-order numerical scheme based on the Adams-Bashforth method is implemented to validate the analytical results. Numerical simulations are conducted using biologically relevant parameters: intrinsic growth rate a = 0.8, transmission rate γ = 0.6, natural death rate of infected prey m = 0.1, natural death rate of predators n = 0.1, and predation-related death rates α1 = 0.3, α2 = 0.2. The predator self-competition rate is set as β = 0.4. Simulation results reveal that reducing the transmission rate γ from 0.6 to 0.4 leads to a 42% reduction in the peak population of infected prey UI(t), while increasing the fractional order from 0.75 to 0.95 decreases predator fluctuations V(t) by 36%, indicating stronger damping due to memory effects. Additionally, a 28% improvement in the survival of susceptible prey US(t) is observed when the predation rate on infected prey α2 is increased, highlighting potential ecological trade-offs. The results confirm the theoretical stability conditions and illustrate how variations in key parameters influence species persistence, disease burden, and predator-prey balance. The proposed model provides a predictive and flexible framework for analyzing eco-epidemiological systems with disease pressure in prey populations and can aid in formulating strategies for ecological disease management.
Keywords |
|
|
|
|
|
|
|
