| Abstrakt: |
Predator-prey dynamical models have been researched generally. In this research, the prey population is divided by two, i.e., susceptible prey and infected prey. We can take the case study of farming system where preys are pests suffering the farmer and species catching preys is a predator. Infected prey happens when susceptible prey is attacked by a virus. Predators can attack infected prey easier than susceptible prey. To remove the number of both of prey, we use prey pesticide as control, and to reduce the number of the predator, we use predator pesticide. Stability and optimal control using pesticides will be analyzed in this research. In predator-prey with infected prey by virus dynamical model, there is a population of susceptible prey, infected prey, predator, and infectious virus assumed countable. From the model of predator-prey with infected prey by a virus, six equilibrium points are determined their stability using eigenvalue. From the model of predator-prey with infected prey by the virus, two controls will be added, i.e., prey pesticide and predator pesticide. An algorithm used for solving optimal control problems and resulting numerical solutions is Forward Backward Sweep Method. In the simulation results, pesticide usage can minimize the number of both prey and predator with a minimum performance index. [ABSTRACT FROM AUTHOR] |
