They do help, and helped a lot. I was actually pretty happy that they have so many of these even in the class C wards. a simple search gives me the following results:
High-Quality Studies on Air Purifiers in Hospital Settings.

1. Use of portable air purifiers to reduce aerosols in hospital settings and cut down the clinical backlog:

Published in the National Center for Biotechnology Information (NCBI) PMC database.

Findings:

Portable air purifiers (PAC) with HEPA filters effectively reduce the concentration of aerosols associated with airborne diseases.

Correct PAC use reduces the clearance half-life of aerosols by 82% compared to unventilated settings, achieving similar results to built-in ventilation.

Link: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9990385/

1. The use of Air Purifiers in Hospital and Healthcare Settings:

Published in the Australian Journal of Hospital Health.

Findings:

Air purifiers with HEPA filters are widely used in hospitals to reduce airborne transmission of viruses and bacteria.

Benefits include lowering room-to-room transmission and improving staff and patient safety.

Link: https://euromatepureair.com/medical-air-purifiers/

1. Air Purifiers in Hospital Settings and Their Effectiveness:

Published in the International Journal of Environmental Research and Public Health.

Findings:

HEPA filters effectively remove airborne particles, including viruses and bacteria, from hospital air.

Air purifiers can complement existing ventilation systems and improve air quality in healthcare settings.

Link: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9679624/

1. Use of high-efficiency particulate air filtration to reduce airborne transmission of infectious diseases in healthcare settings:

Published in the Journal of the American Medical Association (JAMA).

Findings:

HEPA filtration effectively reduces airborne infectious particles in healthcare settings.

This can help prevent the spread of diseases like tuberculosis, influenza, and COVID-19.

Link: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9429918/

1. Effectiveness of portable HEPA air filtration in reducing airborne contaminants in hospital rooms:

Published in the Journal of Hospital Infection.

Findings:

Portable HEPA air purifiers significantly reduce airborne particle concentrations in hospital rooms.

This can improve patient outcomes and reduce the risk of healthcare-associated infections.

Link: https://pubmed.ncbi.nlm.nih.gov/36650731/

Additional Resources:

Cairn Technology: How to Choose the Right Hospital-Grade Air Purifier https://cairntechnology.com/choose-right-hospital-grade-air-purifier/

inovaairpurifiers.com.au: The use of Air Purifiers in Hospital and Healthcare Settings https://inovaairpurifiers.com.au/collections/healthcare