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Computational Ecology and Software, 2021, 11(3): 100-125
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Article

Modeling and analysis of the effects of gaseous pollutants and particulate matters on human health with control mechanisms

Shyam Sundar1, Niranjan Swaroop1, Ram Naresh2, J. B. Shukla3
1Department of Mathematics, Pranveer Singh Institute of Technology, Kanpur-209305, India
2Department of Mathematics, School of Basic and Applied Sciences, Harcourt Butler Technical University, Kanpur-208002, India
3International Internet University for Research, Kanpur-208017, India

Received 18 February 2021;Accepted 25 March 2021;Published 1 September 2021
IAEES

Abstract
Human health is affected by various types of gaseous pollutants (CO, SO2, NOx, etc.) and particulate matters (PM2.5, PM5, PM10) discharged from several sources such as vehicular traffic, small scale production and construction industries etc. in a city. These particulate matters are also discharged into atmosphere of the city by household emissions, causing respiratory diseases and innumerable deaths of the people. Therefore, in this paper, a nonlinear mathematical model is proposed and analyzed to study the effects of gaseous pollutants and particulate matters on human health in a city with control mechanisms. In the modeling process, six dependent variables are considered, namely, the density of human population, the cumulative density of various pollution emitting sources, the cumulative concentration of gaseous pollutants, the cumulative concentration of particulate matters, the cumulative concentration of suitable aerosols sprayed in the atmosphere to neutralize gaseous pollutants and the number density of water drops (amount of water) to wash out particulate matters from the atmosphere. In the modeling process, it is assumed that the human population density is governed by a logistic model, the growth rate of which decreases due to increased cumulative concentration of gaseous pollutants and particulate matters. It is further assumed that the growth rate of cumulative density of various sources discharging pollutants in the atmosphere is proportional to human population density. The cumulative concentration of aerosol sprayed in the atmosphere is considered to be proportional to the cumulative concentration of gaseous pollutants. Similarly the number density of water drops is assumed to be proportional to the cumulative concentration of particulate matters in the atmosphere. The model is proposed in the form of nonlinear ordinary differential equations which are analyzed by using the stability theory. The model analysis shows that in the absence of any control mechanism, the equilibrium level of population density is lower than that when the control mechanisms are applied. The numerical simulation of the model confirms the analytical findings. This study implies that human health is adversely affected without the control mechanism and the death rate of population increases due to various pollutants emitting sources such as vehicular traffic.

Keywords mathematical model;industry;vehicular traffic;gaseous pollutants;particulate matter;external species.


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