# Ecological-economic model for optimal control of fire-driven, semi-arid rangelands

##### Model Description

This is an ecological-economic model that endogenizes discontinuous change between states of fire-driven, semi-arid rangelands which may exist in varying degrees as grassland and woodlands depending partly on the given soil conditions. More sandy soils will result in woodlands, whereas clay soils will more likely result in grasslands. One of the critical features of this model is the existence and impact of fires on these different types of rangelands. Grasslands may build up biomass and create a fireload that once ignited may destroy grass and woodlands. The natural recovery rates of these different rangelands are important in determining the system dynamics.  Without human control through the use of livestock, the equilibrium of the grasslands is determined by their intrinsic growth rates, competition coefficients, as well as their susceptibility to the effects of fire. Accordingly, the model also considers the behavior of fire and herbivores and the interaction between these elements in order to determine optimally controlled management parameters. The time horizon of management planning can heavily influence the pathways and conditions of the system.  Specifically, by controlling the offtake of livestock that grazes on the grasslands, planners may influence the interaction between the grasslands and woodlands to optimal paths which depend not only on natural parameters but also on the time horizons considered and discount rates.

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 $$x$$
This model has four parameters. You can set their values below.
 $$alpha$$ $$beta$$ $$gamma$$ $$u$$
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