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Effects of population and population pressure on forest resources and their conservation: a modeling study

Model Type
SES Library XPP model

in this model, cumulative density of forest resources and population density use generalized logistic models with predatory-prey type nonlinear interactions. The model is an effort to capture not only the effect of population density on forest resources (a logistic model), but also the effect of population pressure on forest resources, which grows proportionally to population density and is limited by the carrying capacity of the forest.  Additionally, it models the effect of economic incentives that incentivize the substitution of other resources for those that would have been harvested from the forest. The system is governed by three dynamic state variables:cumulative density of forest resources, the density of the population, and the population pressure. The model shows that without economic incentives, forest resources will be pushed to extinction but when incentives are included the density of forest resources reaches an equilibrium state (greater than 0). 

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$$\begin{equation}\r dB/dt = sB - \frac{S_0B^2}{L} - \alpha BN - \lambda_2BP\r \end{equation}$$
$$\begin{equation}\r dN/dt = rN - \frac{r_0N^2}{K} + \pi \alpha BN\r \end{equation}$$
$$\begin{equation}\r dP/dt= \lambda N - \lambda_0 P\r \end{equation}$$
$$F(B) = s - \frac{s_0B}{L} - \frac{\alpha K}{r_0}(r + \pi \alpha B) - \frac{\lambda_2 \lambda KB}{\lambda_0 r_0}(r + \pi \alpha B) =0$$
$$dP/dt = \lambda N - \lambda_0 P - \lambda_ 1 PE$$
$$dE/dt = \psi P -\psi_0 E$$
seslib.ode
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