A time-delay model for the effect of toxicant in a single species growth with stage-structure

Abstract

In this paper, we investigate a single-species growth model with stage-structure consisting of immature and mature stages for the effects of toxicants with constant maturation time-delay. We study the dynamics of our model in three cases: an instantaneous emission of toxicant, a constant emission of toxicant, and a periodic emission of toxicant into the environment. We present results on positivity and boundedness of all solutions under appropriate conditions. The model equations are analyzed mathematically with regard to the nature of equilibria and their stabilities using the theory of nonlinear differential equations and computer simulations. It is shown that under suitable conditions, there exists a globally asymptotically stable positive equilibrium. It is concluded from the analysis that as the concentration of toxicant in the environment increases, equilibrium densities of both immature and mature populations decrease. It is also noted that the effects of toxicants are more on the equilibrium level of immature population in comparison to the mature population.