Box fans with HEPA filters are a good immediate and emergency solution but have their drawbacks, mainly:
1) The fan and filter fights against particles coming in from outside, through small cracks under the doors, windows etc. So the higher the outdoor air pollution, the more the fan needs to fight against it. At extremely high pollution levels they will get into problems maintaining healthy air indoors.
2) Sealing the gaps and making your house/room more air tight, increases CO2 levels significantly which leads to drowsyness and decreased mental performance. So you always work with a trade-off.
3) Often you need to run the fans on highest level to be effective which creates quite a high level of noise.
4) Ideally you want something demand controlled that switches automatically on/off or regulates its speed based on the pollution levels.
5) The HEPA filters filter primarily PM2.5 but the wildfires also produce hazardous gases like NOx, VOCs which you would need carbon filters to remove.
With my company AirGradient (we offer open source air quality monitors [1]), we monitor thousands of indoor spaces and the only technology that we found consistently working -no matter of the level of air pollution- are positive pressure systems.
A positive pressure fresh air system takes air from outside, filters it through HEPA/Carbon filters and pumps it into the room. Thereby pressurizing the room and thus preventing dirty air from entering the room.
With this system you just need to achieve a slightly higher pressure then outdoors and then you can consistently achieve zero PM levels inside -even when hazardous outdoors. As a result the system, often runs at low fan speeds and does not create much noise.
Additionally, due to the fact that it uses fresh air, the CO2 levels remain low and you can often add carbon filters to the system.
I made a comparison test of this type of system [2] and a detailed description how it works [3].
[1] https://www.airgradient.com/open-airgradient/kits/
[2] https://www.airgradient.com/open-airgradient/blog/air-purifi...
[3] https://www.airgradient.com/open-airgradient/blog/positive-p...