A mathematical model to study the effects of population pressure on two-patch forest resources

In this paper, we propose a mathematical model of forest resources depletion caused by human exploitation. The human population is comprising of two subpopulations, i.e. nonindigenous people who exploit the forest unwisely (N1) and indigenous people who exploit the forest wisely by considering nondestructive ulitization (N2). The unwise exploitation of the forest resulting in population pressure for the forest. We assume that part of the forest (B1) is managed by the nonindigenous people, while the remaining part (B2) is managed by the indigenous people. It is assumed that the cumulative density of forest resources for each subpopulations and the density of human populations (both indigenous and nonindigenous populations) follow logistic models with predator-prey type nonlinear interaction terms. It is considered that the carrying capacity of forest resources decreases by population pressure. In this paper, we are looking for the effect of different management, especially the population pressure, into the forest dynamics (biomass abundance). A conservation model is also proposed to control the population pressure by providing some economic incentives to people, the amount of which is assumed to be proportional to the population pressure. The model is analyzed by using standard theory of dynamical system and numerical simulation.