Recently, the H5N1 strain of avian influenza (“bird flu”) has sparked fear of a potential pandemic. As the world of science trains a careful eye on the development of the virus, the world of mathematics, too, can play a role. For example, the applet below can help predict the spread of a virus over a population. Each person may pass on a germ or virus to others with whom they come in contact, but the disease will not be transmitted if the recipient has a resistance to the disease, has had a vaccination, or has already been infected. Consequently, there is a “population of opportunity” to whom the disease can spread.
The spread of a virus is influenced by four factors:
- the size of the population of opportunity;
- the number of days contagious;
- the number of people with whom an infected person comes in contact; and,
- the probability of contracting the virus from contact with an infected person.
The following applet starts with one person infected. After that, the disease will spread or die out based on your settings.
Activities
- Infected individuals can spread the flu virus from the day before they begin to feel ill until 3–7 days after the start of flu symptoms. Use these numbers to examine the model in the applet.
- If the simulation is run multiple times (without changing the settings), how does the percent infected change?
- Change the population size, but do not change the other values. Does the percent of people eventually infected change?
- What settings cause the infection to die out quickly, with a low percentage infected?
- What settings cause the infection to spread quickly over time, with a high percentage infected?
- Can you change the settings so that about 80% of the population is eventually infected? What about 50%? And 20%?
- Can you change the settings so the disease runs for a long time—more than 60 days?
- How would you change the settings to model
- Isolating sick people?
- Vaccinating healthy people?