Why is it rare for a person to have 2 (or more) infectious diseases (for example: Flu & Cold together at the same time)?
Although it's rare, it happens when the immune system is weak (e.g when patient has both AIDS and Kaposi's sarcoma).
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What makes you consider it is rare? It is not at all uncommon to be affected by two infections. Typically I agree we aren't as the number of infectious organisms that we are exposed to which cause a clinical manifestation (i.e. aren't controlled by the immune system) are low. Nevertheless, any chronic infections such as herpes viruses may often manifest when we are under stress with another infection, many bacterial pneumonias are more likely to occur when a viral infection is also present and of course the many immunosuppressed people. Arguably a lot of infections are by two or more causative agents as often if one is able to enter where it shouldn't, another may, but one is likely to be more dominant. Furthermore even our infections can get infections with bacteriophages infecting the bacteria we are infected with.
Secondary infection is not rare at all. I mean consider babies. When they get the cold their immune system is weak and focused on the cold virus and they can get viral pneumonia from the flu very easily for example.
TB is another good example of a disease often weakening the immune system and raising the probability of a secondary infection and HIV is a viral one with the same weakening and higher probability of secondary infection.
Another example where coinfections are common is with tick-borne illnesses.
One 2006 review suggests that in some regions of North America the prevalence of Ixodes ticks carrying two pathogens may be up to 28% and that from 4-45% of humans with Lyme disease also appear to have ehrlichiosis or babesiosis(Coinfections Acquired from Ixodes Ticks).