A mathematical model of Chenopodium album L. dynamics under copper-induced stress

Abstract

Heavy metal contamination of the soil is a global problem that produces different harmful effects from an environmental and public health perspective. Although there have been numerous efforts to solve this problem, there is no precise methodology to decontaminate heavy-metal polluted soils. One of the strategies to develop such methods relies on mathematical modelling. Pursuing this goal, we propose a novel mathematical compartmental model consisting of a linear system of differential equations to address the suitability of the model plant (Chenopodium album L.) for the remediation of contaminated areas, such as sewage sludge lagoons. Our results show a tendency to maintain high concentrations of copper (Cu) in the roots with the possibility of continuing with good plants' dynamics. Moreover, the model theoretically proposes contaminant concentration in the plants' shoots and roots and predicts a more prolonged tendency to accumulate copper concentrations in the shoots and disrupt the shoots' dynamics. These results provide complementary support for the suitability of this model plant to be used in contaminated areas. In addition, we present asymptotic tendencies of the plants' biomass content and nitrogen-assimilatory (Nitrate reductase; NR) enzyme activity. In this way, we project the relationship between contaminant accumulation and plants' measurements. These projections are essential as they can potentially be used for optimization purposes and strategic harvesting planning. Finally, we present a parameter sensitivity analysis to complement the model examination.