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.