What would a modern day plague look like?

If there was a plague today, it would be catastrophic or very short and quite small. Because of technological advances and new medication, the world has been good at suppressing a plague and quick with dealing with possible plagues, such as the swine flu. If a plague were to start today, as long as the world reacted quickly (unlike the government in Oran), it should be able to be contained. The other possible outcome of the plague could be almost apocalyptic. Technological advances can also spread the plague. People commute between places easily and therefore more people can come into contact with someone who is contagious. If someone who had the plague got on a plane, that person could infect many there and then infect even more people at the location they're traveling to. Transportation is easy to access, yet easy to spread diseases.
It depends on how the population would react as well. If everyone listened to the government and any regulations they set forth to contain the plague, theoretically the plague should be contained and not turn into a global plague.
In today's day, many areas don't have as many rats as other ages did. The rats often spread diseases. The fleas that diseased them looked for new hosts and then when there were no other viable sources of blood, they moved to humans. Because there are less rats in many affluent areas, the people there are in less of a danger. Unfortunately this is not the case globally. Humans don't have any natural resistance against this. In the case of rats, the ones with natural immunity survive and pass on this immunity through generations. Humans haven't been exposed to recent rats' diseases and therefore haven't acquired immunity. Thankfully, due to modern technology, scientists can create vaccinations to help increase our immunity and they can do so quickly. There are scientists specifically to try to prevent the spread of illnesses. Hopefully we have learned from past mistakes and will be able to prevent a global plague.

For more information about a modern day plague:
http://science.howstuffworks.com/life/cellular-microscopic/plague5.htm

Does the plague desensitize death?

The plague does desensitize death. At first, the other citizens care about the funerals and how the dead are being buried. The government cares as well and tries to keep the funerals similar to usual, but soon efficiency and speed become higher concerns. The funerals are shortened and scheduled at night. There is no ceremony, no relatives or friends participating. But they keep track of them. This is considered successful, which shows the authority's lowered standards. Eventually there is no space left and no time to make more space so the bodies are carried by train to the crematorium. The government tries to keep the population in the dark about this, but they catch on and some hide by the tracks of the passing train and toss flowers in. This shows humanity is left, and that there are attempts to make the funerals at least the tiniest bit more "tasteful." Optimism changes and people are okay with this funeral process because it grew no worse. Their thinking changes from "How do I want to be buried and how do I want my funeral to go?" to "Good enough" or something along the lines of how these funerals are still at least better than a dog's funeral.
Their thinking of death changes as well. They become numb to it. It is around them all the time and the chances of someone's loved one dying are very high. It's similar to what Viktor Frankl says in "Man's Search for Meaning." In the concentration camps, people eventually stopped reacting to bad situations or death. The same thing happens during the plague. The memories of loved ones fade, their emotions are much less intense. Everyone's adapting to the plague. There is no other way to keep living in that situation, according to the narrator of "The Plague." Everyone lives in the present moment. One can't think of the future much because the uncertainty of the future is clear in a situation like this one. In drastic situations, drastic and abnormal things happen and that is to be expected: that the unexpected will happen.