Maximizing tree harvesting benefit from forests under insect infestation disturbances

Mathematical modeling has been recognized as an important tool to advance the understanding of the synergetic effect of coupled disturbances (stressors) on the forest population dynamics. Nonetheless, most of the modeling done on disturbances focus on individual disturbance agents and the modeling research on disturbances interactions uses predominantly descriptive statistical processes. This state of art points to the need for continuing modeling efforts not only for addressing the link among multiple disturbances but also for incorporating disturbance processes. In this paper, we present an age-structured forest-beetle mechanistic model with tree harvesting. We investigate three scenarios involving the beetles equilibrium states (no beetles, beetles in endemic and epidemic states). Optimal control theory was applied to study three different benefit functions involving healthy and dead trees. The numerical simulations show that maintaining the beetle infestation at endemic level instead of eliminating all the beetles is sufficient to ensure the forest has trees with all ages. Furthermore, the numerical simulations shows that the harvesting benefit decreases as the number of beetles increases in all cases except when the benefit functional includes a cost (ecological and harvest implementation) and the value of wood is equal across all trees (healthy harvested trees, trees killed by beetles, and trees that die naturally).