Document Type : Research Article

Authors

• Mahnaz Abedini ¹
• Gorbanali Haghighatdoost ¹
• Hossein Kheiri ²

¹ Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

² Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran

Abstract

This study develops and analyzes a four-compartment predator–prey model incorporating disease dynamics and optimal control. The first prey population follows logistic growth and is susceptible to infection, whereas the second prey population remains disease-free and exhibits greater competitive ability. The model incorporates an epidemic process within the first prey population and considers two control measures: reducing disease transmission and treating or removing infected individuals. We investigate the resulting system theoretically to assess the effects of these interventions on disease prevalence, prey persistence, predator dynamics, and ecosystem stability. In particular, stability analysis, sensitivity analysis, and optimal control theory are employed to characterize the model dynamics and identify the most influential parameters. The results indicate that the carrying capacity (k), infection rate (γ), and disease-induced mortality rate (µ) play major roles in determining the persistence of infection. Moreover, the optimal isolation (u₁) and treatment (u₂) strategies substantially reduce disease prevalence, increase the healthy prey population, and promote predator stability compared with the uncontrolled scenario. Numerical simulations further demonstrate the effectiveness of the proposed control strategies in mitigating infection and maintaining ecological balance. These findings demonstrate that the model provides a unified framework for examining the interactions between heterogeneous prey populations, disease transmission, predation, and targeted control interventions.

Highlights

• Develops a four-compartment eco-epidemiological model integrating two prey populations (one susceptible to infection, one disease-free and competitively superior) with a generalist predator, incorporating asymmetric disease dynamics.
• Implements and compares two time-dependent intervention measures—isolation (to reduce disease transmission) and treatment (to remove infectious individuals)—within a unified optimal control framework.
• Identifies carrying capacity (k), infection rate (γ), and disease-induced mortality (µ) as the most influential parameters governing infection persistence, using global LHS-PRCC sensitivity analysis.
• Rigorously establishes existence, positivity, boundedness, and local/global stability conditions for all equilibrium points, including disease-free, predator-free, and coexistence states.
• Numerical simulations show that combined optimal isolation and treatment significantly reduce infection prevalence (by up to 25%), enhance healthy prey populations, and stabilize predator densities compared to uncontrolled scenarios, without destabilizing ecosystem balance.

Keywords

• Predator-prey model
• Prey infection
• Optimal control
• Stability analysis
• Sensitivity analysis

Main Subjects

• Optimal Control