Mathematical model to study the effects of primary and secondary pollutants on biological population

Abstract

A nonlinear mathematical model is presented here to analyze the effects ofair pollutants present in the environment on biological population. To studythis, a susceptible - diseased class of population is considered in whichthe susceptible becomes infective when comes in contact with primary andsecondary forms of air pollutants present in the atmosphere. The primarypollutant is taken to be emitted from an external source with a constantemission rate and a part of which is transformed into secondary pollutant.The stability theory of differential equations is used to analyze theproposed model and to substantiate these analytical findings numericalsimulation is also developed using fourth order Runge - Kutta Method. It ispointed out that the density of diseased population increases if emission rate ofprimary pollutant and its transformation rate to secondary pollutantincreases and their effects on biological population show differentquantitative behaviour with change in uptake concentration and toxicity ofthese pollutants.