The impact of air ventilation systems on airborne virus transmission (AVT), and aerosols in general, in confined spaces is not yet understood. The recent pandemic has made it crucial to understand the limitations of ventilation systems regarding AVT. We consider an elevator as a prototypical example of a confined space and show how ventilation designs alone, regardless of cooling or heating, contribute to AVT. Air circulation effects are investigated through multiphase computational fluid dynamics, and the performance of an air purifier in an elevator for reducing AVT is assessed. We have investigated three different flow scenarios regarding the position and operation of inlets and outlets in the elevator and a fourth scenario that includes the operation of the air purifier. The position of the inlets and outlets significantly influences the flow circulation and droplet dispersion. An air purifier does not eliminate airborne transmission. The droplet dispersion is reduced when a pair of an inlet and an outlet is implemented. The overall practical conclusion is that the placement and design of the air purifier and ventilation systems significantly affect the droplet dispersion and AVT. Thus, engineering designs of such systems must take into account the flow dynamics in the confined space the systems will be installed.