Portable air purifiers have been extensively used to improve indoor air quality and mitigate the transmission of airborne diseases. However, the efficacy of mitigation is strongly affected by the interactions between jet flows of processed air from the air purifiers and the background airflows driven by the ventilation system. Critical factors in this context include the position and capacity of air purifiers and the ventilation rate of the heating ventilation and air-conditioning (HVAC) system. These factors are investigated in this study via computational fluid dynamics (CFD) simulations and the infection probability for different scenarios is quantified using the latest airborne infection predictive model incorporating recent pathological and clinical data for SARS-CoV-2. The results show that the use of air purifiers can significantly reduce the concentration of particulate matter, thus contributing to a generally lower risk of airborne transmission. However, the position of air purifiers affects their overall efficacy remarkably. Comparatively, a central HVAC system is more efficient at removing airborne particles under an equivalent ventilation rate assuming it uses a mixing ventilation scheme.