Modeling effects of primary and secondary toxicants on renewable resources

Abstract

In this paper a nonlinear mathematical model to study effects of primary and secondary toxicants on the biomass of resources such as forestry, agricultural crops, etc., is proposed and analyzed. The primary toxicant is emitted into the environment with a constant prescribed rate by an external source and a part of which is transformed into a secondary toxicant, which is more toxic, both affecting the resource simultaneously. By using stability theory of differential equations, it is shown that the biomass density of resource attains an equilibrium level, the magnitude of which is smaller than its original (toxicant independent) carrying capacity and it decreases as the emission rate of primary toxicant increases. It is also shown that the decrease in biomass density of resource is more than the corresponding case of a single toxicant due to large transformation and uptake rates and high toxicity of secondary toxicant. It is pointed out that the resource may even become extinct if emission rate of primary toxicant and transformation rate of secondary toxicant are very large and their effects on resource are sufficiently harmful due to large uptake and high toxicity of secondary toxicant which is more toxic