Modelling the effect of traffic pollutants on human population with a control strategy
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ORIGINAL ARTICLE
Modelling the effect of traffic pollutants on human population with a control strategy J. B. Shukla1 · Niranjan Swaroop2 · Shyam Sundar2 · Ram Naresh3 Received: 2 January 2020 / Accepted: 21 May 2020 © Springer Nature Switzerland AG 2020
Abstract The emission of traffic pollutants such as sulphur dioxide, carbon monoxide, nitrous oxide and particulate matters in the atmosphere of a city affecting human population is one of the main concerns and needs attention in the present scenario. The removal of these pollutants affecting human population adversely is, therefore, very much desirable. In this paper, a nonlinear mathematical model is proposed to study the effect of traffic pollutants on human population with a subsequent control strategy in the form of introduction of liquid (water) drops for removal of these pollutants from the atmosphere. In the modelling process, four dependent variables are considered, namely the density of human population adversely affected by the traffic pollutants, the cumulative density of traffic (vehicles) which is human population density dependent, the cumulative concentration of traffic pollutants and the number density of liquid drops introduced in the polluted atmosphere to remove these pollutants. It is assumed that the cumulative concentration of traffic pollutants is directly proportional to the cumulative density of traffic (vehicles), the growth rate of which is dependent on the density of human population. It is also assumed that the growth rate of liquid drops introduced in the atmosphere to remove traffic pollutants is directly proportional to the cumulative concentration of these pollutants. The model is analysed using stability theory of differential equations and numerical simulation under two cases, viz. without control strategy and with control strategy using liquid drops. The analysis of the model reveals that due to the increase in the cumulative concentration of traffic pollutants as a result of increased traffic density, the human population is adversely affected. Further, when a control strategy in the form of introduction of liquid drops is applied to remove these pollutants, the cumulative concentration of traffic pollutants decreases leading to the increase in the density of human population. The numerical simulation has also been performed to confirm these results. Keywords Mathematical model · Human population · Traffic density · Traffic pollutants · Liquid drops · Stability · Simulation
Introduction The vehicular air pollution is one of the prime concerns in view of continuously deteriorating air quality and subsequently responsible for various health hazards. The deleterious health effects caused by major vehicular pollutants * Shyam Sundar [email protected] 1
International Internet University for Research, Kanpur 208017, India
2
Department of Mathematics, Pranveer Singh Institute of Technology, Kanpur 209305, India
3
Department of Mathematics, School of Basic & Applied Sciences, Harcourt Butler Technical University, Kanp
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