It may be true that 2,000 years ago sickness was understood to be the result of demons or sin, and in many cases it was (and is).
HOWEVER, Jesus is truth. In truth, sickness can befall the most righteous person on this planet (or the most sinful) purely as a natural consequence of living in a world with bacteria. A lot of the Pentecostal brand Christians teach that if you are sick then something is wrong because a person who truly follows God can’t get sick. This is simply not true. Of course all people that truly follow God are still sinful, but that doesn’t detract from the point.
Is Katrina the punishment for sin, or an example of the natural consequences of sin? Maybe, but it’s a huge mistake to say it has to be. It’s weather. Weather is a natural process which does just happen aside from divine intervention. God can control is, but He usually doesn’t.
Now, did Adam and Eve suffer bad weather in the garden of Eden? Probably not, because that wouldn’t be Eden. I think it would be fair to say that bad weather itself came as something God instituted because of sin. What about bacteria? Did Adam and Eve get sick before the fall? Probably not. However, bacteria, just like the weather, is a natural process which works without divine intervention (though God can operate it if He chooses to.) I think it would be probable that the existence of bacteria itself was something God put into play because of the fall.
Now ask yourself is Jesus can suffer because of sin. The answer is a resounding yes! The crucifixion itself was an example of Jesus suffering because of sin. He probably suffered a lot in the rest of His life because if it, too. People probably shunned Him and treated Him badly and all sorts of things. He suffered because of their sin. Jesus suffering from the cold then would be His suffering from other people’s sin which brought about the existence of the natural process of the cold virus.
We are called to suffer in our lives and to bear the results of sin, both our own and others’. Jesus could have done no less in His life. He had to come into a world with bad weather and with disease because of other peoples’ sin (Adam and Eve.) This doesn’t mean He sinned himself.
Jesus is fully human. The human body is the human body. Jesus didn’t have some special supernatural body. Bacteria is bacteria. God can cause bacteria to harm a person or prevent it from happening, but He usually doesn’t. When a person gets sick they usually just get sick because that’s how the natural world works. Jesus was born into and was a part of this natural world.
Just because it may have caused His desciples to doubt Him, Christ would not have been kept safe from illness by God. God doesn’t change truth just because someone is going to misunderstand it. Jesus taught about the Eucharist even though thousands left because of it. He didn’t change the truth just because it scandalized those people. The truth is the truth of the natural world.