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This study is motivated by the amplified transmission rates of the SAR-CoV-2 virus in areas with high concentrations of fine particulates (PM 2.5) as reported in northern Italy and Mexico. To develop a deeper understanding of the contribution of PM 2.5 in the propagation of the SAR-CoV-2 virus in the population, the deposition patterns and efficiencies (DEs) of PM 2.5 laced with the virus in healthy and asthmatic airways are studied. Physiologically correct 3-D models for generations 10–12 of the human airways are applied to carry out a numerical analysis of two-phase flow for full breathing cycles. Two concentrations of PM 2.5 are applied for the simulation, i.e., 30 μg⋅m−3 and 80 μg⋅m−3 for three breathing statuses, i.e., rest, light exercise, and moderate activity. All the PM 2.5 injected into the control volume is assumed to be 100% contaminated with the SAR-CoV-2 virus. Skewed air-flow phenomena at the bifurcations are proportional to the Reynolds number at the inlet, and their intensity in the asthmatic airway exceeded that of the healthy one. Upon exhalation, two peak air-flow vectors from daughter branches combine to form one big vector in the parent generation. Asthmatic airway models has higher deposition efficiencies (DEs) for contaminated PM 2.5 as compared to the healthy one. Higher DEs arise in the asthmatic airway model due to complex secondary flows which increase the impaction of contaminated PM 2.5 on airways' walls. [Display omitted] • Deposition of PM 2.5 laced with the virus in healthy and asthmatic airways was studied. • 3-D models for generations 10–12 of the human airways were applied. • Two concentrations of PM 2.5 of 30 and 80 μg⋅m−3 were applied for the simulation. • Asthmatic airways had higher deposition for contaminated PM 2.5 than healthy ones. • Higher DEs in asthmatic airways were due to complex secondary flows. [ABSTRACT FROM AUTHOR]