Malaysian Journal of Mathematical Sciences, May 2018, Vol. 12, No. 2
Optimal Control for a Predator-Prey Model with Disease in the Prey Population
Simon, J. S. H. and Rabago, J. F. T.
Corresponding Email: jhsimon@up.edu.ph
Received date: 15 May 2017
Accepted date: 28 March 2018
Abstract:
In this study, an optimal control problem is formulated to a predatorprey model with disease in the prey population. This model is an adapted Lotka-Volterra model but with an applied SI epidemic dynamics on the prey population. Two controls are then applied to the system: first, a separating control, that is intended to separate the sound prey from the infected prey population, and the other serves as a treatment control that is to decrease the rate of death caused by the disease. We then formulate a finite-time horizon optimal control problem by minimizing the infected prey population at the final time and the cost induced from the application of the controls. Characterisation of the optimal controls is done using Pontryagin’s Optimality Principle by introducing the Hamiltonian with the associate adjoint variables. Using varied set of parameters, we analyse numerical simulations showing different scenarios from the system. The simulations are obtained using a forward-backward sweep method on the first order necessary conditions for the control problem.
Keywords: optimal control, predator-prey, Pontryagin optimality principle, forward-backward sweep method
