On the spread of ultrafine particulate matter: A mathematical model for motor vehicle emissions and their effects as an asthma trigger

Asthma is a respiratory disease that affects the lungs, with a prevalence of 339.4 million people worldwide G. Marks, N. Pearce, D. Strachan, I. Asher and P. Ellwood, The Global Asthma Report 2018, globalasthmareport.org (2018)]. Many factors contribute to the high prevalence of asthma, but with the rise of the industrial age, air pollutants have become one of the main Ultrafine particles (UFPs), which are a type of air pollutant that can affect asthmatics the most. These UFPs originate primarily from the combustion of motor vehicles [P. Solomon, Ultrafine particles in ambient air. EM: Air and Waste Management Association's Magazine for Environmental Managers (2012)] and although in certain places some regulations to control their emission have been implemented they might not be enough. In this work, a mathematical model of reaction-diffusion type is constructed to study how UFPs grow and disperse in the environment and in turn how they affect an asthmatic population. Part of our focus is on the existence of traveling wave solutions and their minimum asymptotic speed of pollutant propagation c(min). Through the analysis of the model it was possible to identify the necessary threshold conditions to control the pollutant. emissions and consequently reduce the asthma episodes in the population. Analytical and numerical results from this work prove how harmful the UFEs are for the asthmatic population and how they can exacerbate their asthma episodes.