eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2019-02-03 7 2 65 74 10.12691/ajams-7-2-3 AJAMS2019723 article Shyam Sundar ssmishra_75@yahoo.co.in 1 Niranjan Swaroop 1 Ram Naresh 2 Department of Mathematics, Pranveer Singh Institute of Technology, Kanpur, India Department of Mathematics, School of Basic and Applied Sciences, Harcourt Butler Technical University, Kanpur, India It is well known that the human health is adversely affected by toxic air pollutants such as sulfur dioxide, nitrous oxide etc. present in the atmosphere. The removal of such pollutants from the atmosphere is, therefore, very much desirable. In this paper, a nonlinear mathematical model is proposed to study the population density dependent industrial emission of toxic air pollutants in the atmosphere and their removal by spraying liquid (water droplets) and particulate matter. In the modeling process, five variables are considered, namely; the cumulative concentration of toxic air pollutants, the density of human population affected by the toxic pollutants, the density of industrialization which is population density dependent, the number density of liquid droplets sprayed in the environment and the density of particulate matter sprayed in the environment. It is assumed that the emissions of toxic air pollutants are linearly related to the density of industrialization, the growth rate of which is directly proportional to the density of human population. It is also assumed that the growth rate of externally sprayed species in the environment is directly proportional to the concentration of toxic air pollutants in the environment. The model is analyzed using stability theory of nonlinear differential equations and numerical simulations. The model analysis shows that as the rate of spray of external species in the environment increases, the cumulative concentration of toxic air pollutants decreases. It is also found that as the rate of removal of toxic pollutants increases, the cumulative concentration of toxic air pollutants in the environment decreases. The effect of toxic air pollutants is observed to decrease the density of human population. The numerical simulation confirms analytical results. http://pubs.sciepub.com/ajams/7/2/3/ajams-7-2-3.pdf non linear mathematical model pollutant particulate matter industrialization stability