Modeling the effect of an intermediate toxic product formed by uptake of a toxicant on plant biomass

In this paper, a nonlinear mathematical model is proposed and analyzed to study the effect of an intermediate toxic product on the growth of plant biomass. It is assumed that the toxicant uptaken by plant biomass interacts with water (sap) present in it and forms an intermediate product, which then affects the biomass. To model the phenomena, it is further assumed that the intermediate product decreases the intrinsic growth rate of biomass density while the environmental concentration of toxicant decreases its carrying capacity. The model is analyzed using stability theory of differential equations and numerical simulation. It is shown that as the rate of emission of toxicant increases, the equilibrium level of plant biomass decreases, but this effect is determined by the emission rate of toxicant in the environment, the rate of its uptake as well as by the rate of formation of the intermediate toxic product.