Answered by the Egyptian House of Fatwa
The Question:
What is the ruling of the Shari’ah for individuals with infectious diseases such as influenza who frequent mosques to pray and spread the disease like wild fire among those praying in the mosques?
The Answer:
Islam takes into consideration the life and health of Muslims and forbids people from killing each other. Allah the Almighty says: Do not kill each other, for God is merciful to you [4:29], … Do not contribute to your destruction with your own hands, but do good, for God loves those who do good [2:195]. The Messenger of Allah 
said: “Do not cause harm and do not reciprocate harm” [Ibn Majah].
One of the established legal maxims is to ‘undertake the lesser harm to ward off the greater’. Therefore, if a Muslim comes down with an infectious disease, he must avoid mixing with others so as not to spread it among them. He must pray in his home until Allah, the Almighty, cures him; there is no harm in this because the Messenger of Allah said: “If a land is stricken by plague, do not enter it; and if it is stricken by plague while you are in it, do not depart from it” [Ahmed]. This is what is known today as quarantine.
If eating food with offensive smells is a reason for abandoning congregational prayers to prevent harming others, then abandoning congregational prayers for fear of transmitting infectious diseases and harming those who are praying comes first.
Allah, the Almighty, knows best.
Does this include the common flu or cold?
Salam Alaikum.
What about bad odor? Is it reason enough to skip congregational prayers?
It would only make sense if it included the common cold because so many people have it throughout the year, probably one that most people are careless about, and the germs tend to survive on surfaces for a couple of days (meaning it can be spread quite easily). But that’s just my opinion.
Remember to get your flu shots! 🙂
Assalaamu’alaikum,
The Prophet (PBUH) recocommended his followers to not enter the masjid right after eating onions or garlic. In the form of bad oder, it really is a matter of ettiquites.
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