Modeling the effect of toxicant on the deformity in a subclass of a biological species

Abstract

In this paper, a nonlinear mathematical model to study the effect of a toxicant on a biological population is proposed and analyzed. We have taken the case in which some members of a biological population get severely affected by the toxicant and show abnormal symptoms, like deformity, fecundity, necrosis, etc. It has been assumed that the toxicant is produced by the population itself. This model can be applied to the human population which creates pollution and affects itself. The analysis of the model suggests the need of a regulatory agency to control the emission of toxicant from manmade projects. The stability analysis of the equilibria of the proposed model and existence of Hopf-bifurcation are determined. We have also determined the direction and stability of bifurcating periodic solutions to clearly understand the effect of emission rate of the toxicant on the biological species. Finally, numerical simulation has been given to illustrate the mathematical results.

The effect of an external toxicant on a biological species in case of deformity: a model

“…They have proposed and analyzed mathematical models by considering different cases, such as effect of a single toxicant or more than one toxicant on biological species, allelopathy case, deformity in a subclass of species, etc. (Freedman and Shukla 1991;Shukla and Agrawal 1999;Shukla et al 2003;Agrawal and Shukla 2012;Kumar et al 2016), to provide important insights for the effect of toxicants on biological species. In particular, Freedman and Shukla (1991) have studied the effect a single toxicant on a species with a consideration that toxicant affected on the growth rate and decreasing the carrying capacity of the environment.…”

“…Here, it is assumed that toxicant is emitted in the environment from some external source. Further, understand the case of deformity after-effect of a toxicant in more meaningful manner, Kumar et al (2016) proposed and analyzed a model with an assumption that toxicant emitted by biological species itself. They have shown, toxicant decreased the total population density and a subclass of species suffers from deformity.…”

A Model for the Adverse Effect of Two Toxicants Causing Deformity in a Subclass of a Biological Species

“…The research works have been carried out for different cases such as effect of a single toxicant, more than one toxicant, on a biological species or two biological species with a competition of thrives in the same environment etc. Further, a highly important phenomenon that is after-effect of toxicants a subclass of biological species shows deformity, was studied ( [1], [5]). Agrawal et al [1] proposed a model to study the effect of a single toxicant emitted from some external sources, on a biological species in which a subclass of biological species having abnormal symptoms and not capable in reproduction.…”

“…Agrawal et al [1] proposed a model to study the effect of a single toxicant emitted from some external sources, on a biological species in which a subclass of biological species having abnormal symptoms and not capable in reproduction. In addition, Kumar et al [5] proposed and analyzed a modified model to study the effect of a toxicant on a produced by the biological species itself, in which a subclass of biological species is severely affected.…”