Stress can affect your health; it seems to compromise your immune system. So even if it doesn’t directly make you sick it leaves you open to picking up an illness from somebody else. If other people come to work sick that put you at risk.
Poor ventilation exacerbates the problem. You can combat this by airing out the office whenever possible (which is difficult in winter as you want to keep the warm air in) and putting in plenty of green plants.
Problem areas for germ cross-infection include anywhere used by several people during the day. Water-coolers, kitchen areas, tea and coffee utilities, communal telephones, computer keyboards and communal printers are all high touch points that carry germs for the last ill person who used them. But knowing this means you can disinfect them. Use disinfectant spray during the day. When you use a regular office cleaning service they tend to give more attention to these areas anyhow, but unless they are there all the time the germs will build up.
If you use a regular cleaning service you are probably coming out ahead. Sick-days cost your company money, in paid time off, in lost production, and in potential lost business opportunities. If members of your staff do come in sick they may well cause others to take time off. An office cleaning service can easily minimise these issues.