Rosado Pérez, Michelle N.

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    Modeling the spread of ultrafine particulate matter emitted by motor vehicles, their effects as asthma triggers with a result of optimal control
    (2020-12-08) Rosado Pérez, Michelle N.; Ríos Soto, Karen R.; College of Engineering; Steinberg, Lev; Cabrera Ríos, Mauricio; Ortiz Bermúdez, Patricia; Córdova Figueroa, Ubaldo M.; Other; Rodríguez Román, Daniel
    The Global Burden of Diseases estimated asthma prevalence to be 339.4 million people worldwide in 2016 alone, being air pollutants one of its main causes. Ultrafine particulate matter (UFP) are air pollutants that affect the asthmatic population and as a consequence of its spread, exacerbate their asthma episodes. Ultrafine particles are particles with aerodynamic diameters of less than 0.1 μm that originate primarily from motor vehicles combustion. UFPs have not been well studied even though they are considered as the most dangerous type of particulate matter. On the other hand, many countries, including the United States and Puerto Rico, have no regulations that control their emissions. In order to study this problem, a mathematical model of nonlinear partial differential equations of reaction diffusion-advection type is introduced to show how the UFPs growth and disperse in the environment as a result of motor vehicle emissions, and in turn, how it affect an asthmatic population. Traveling wave solutions are assumed as an approach to solve and analyze the model, including a minimal speed of pollutants propagation. Equilibrium points for the system are found, as well as a threshold condition named Rp, that establish whether motor vehicles emissions will affect the asthmatic population. Numerical simulations were also performed, with parameter values obtained from the literature, which aid to identify which conditions are necessary to control the pollutants emissions and reduce the asthma episodes. This work confirms that the growth rate of pollutant emissions must be reduced in order to decrease the concentrations of UFPs in the environment. Similarly, the UFPs inhalation rate by humans should also be decreased to reduce the asthma incidence and prevalence. The use of filters on motor vehicles and face masks for the asthmatic population may be alternative methods of control to reduce UFP emissions and asthma episodes in the population, respectively. Through optimal control theory, the effects of these control measures were studied.