A Killer Virus You have volunteered for the Peace Corps and have been sent to Rwanda to help in humanitarian aid. You meet with the World Health Organization (WHO) and find out about a new killer virus, Hanta. If just one copy of the virus enters the human body, it can start reproducing very rapidly. In fact, the virus doubles its numbers in 1 hour. The human immune system can be quite effective, but this virus hides in normal cells. As a result, the human immune response does not begin until the virus has 1 million copies floating within the body. One of the first actions of the immune system is to raise the body temperature, which in turn lowers the virus replication rate to 150% per hour. The fever and then flu-like symptoms are usually the first indication of the illness. Some people with the virus assume that they have only a u or a bad cold. This assumption leads to deadly consequences because the immune response alone is not enough to combat this deadly virus. At maximum reaction, the immune systems alone can kill only 200,000 copies of the virus per hour. Model this initial phase of the illness (before antibiotics) for a volunteer infected with 1 copy of the virus.

a. How long will it take for the immune response to begin?

b. If the number of copies of the virus reaches 1 billion, the virus cannot be stopped. Determine when this happens.

c. When the number of copies of the virus reaches 1 trillion, the person will die. Determine when this occurs. To combat this virus fully, the infected person needs to receive an injection and hourly doses of an antibiotic. The antibiotic does not affect the replication rate of the virus (the fever keeps it at 150%), but the immune system and the antibiotics together kill 500,000,000 copies of the virus per hour.

d. Model the second phase of the virus (after the antibiotics are taken). Determine the latest time at which you can start administering the antibiotic in order to save the person. Analyze your model and discuss its strengths and weaknesses. (See enclosed CD for the UMAP module.)