A mathematical evolution model for phytoremediation of metals

In the past few decades, efforts have been made to clean sites polluted by heavy metals such as chromium. One of the new innovative methods of eradicating metals from soil is phytoremediation. Phytoremediation uses plants to pull metals from the soil through the roots. This article develops a system of differential equations to model the plant metal interaction of phytoremediation. We prove there exists a threshold time, $t$*, where the amount of metals in the environment meet a prescribed EPA criteria. The cost of phytoremediating up to time $t$* is computed. The cost function can be used to estimate the feasibility of clearing a polluted site through phytoremediation as opposed to alternate techniques such as brown filling.