Internal and external sources for epidemic spread

Several countries have had outbreaks of swine flu in recent weeks. Many accounts say that the disease emerged in Mexico, passed to other countries when travellers left, and then started spreading within the new countries.

Mexico can provide a steady source of cases for the new countries, limited by the number of people travelling out of Mexico to them. Once in the country, people can pass the disease on to other people. When there are a small number of people with the disease, the rate of internal spread is small, being no greater than the number of people who they meet, and less than the number of people who have brought the disease from overseas. Over time, the internal rate of transfer picks up and overtakes the external source. The exact overtaking time and the pattern of emergence depend on the effectiveness of transfer, number of foriegn travellers, and other factors.

There is an analogy between flu spread and technology transfer. Early on in a technology's life, it may be acquired from abroad for example through trade links. As time passes, people are exposed to the technology through domestic contact and internal transfer can overtake foreign transfer, dependent on factors like whether the technology can be easily learned.

The graph shows the influences of external and internal sources for technology spread along an S-shaped curve. The external source (the straighter line) is earlier more important, and there would be no spread at all without it. The internal source (the curvier line) becomes more important after a while, and accounts for most of the spread from then.