Optimal Control Strategies in a Diseased Prey–Predator Model With Holling Type-II Dynamics

In this study, an optimal control problem is formulated to a prey–predator model with disease in both species. The model is an adapted Lotka–Volterra model by incorporating susceptible–infected (SI) epidemic dynamics on the prey–predator population. A sensitivity analysis is conducted. The result of the analysis shows that the infection rates β1 and β2 and the conversion rate e1 are critical, influencing the dynamics through interaction and efficiency. The time-dependent control is implemented in the system to determine the most effective disease control strategy. The optimal control is characterized using Pontryagin’s optimality principle, which involves introducing the Hamiltonian and its associated adjoint variables. The study found that separating infected populations is crucial for disease elimination. We examine numerical simulations of various system scenarios using a wide range of parameters. Simulations are performed using a forward–backward sweep method with first-order necessary conditions for the control problem. The optimal solution is determined through numerical methods. The findings indicate that the ideal combination of the three control strategies necessary to meet the specified objective is influenced by the relative costs associated with each control measure. A detailed discussion of the simulation results is provided.