The native Hawaiians lived for centuriesin isolation from other peoples. When foreigners finally came to the islands they brought with them diseases such as measles, whooping cough, and smallpox, which decimated thepopulation. Suppose such an island has a native population of 5000, and a sailor from a visiting ship introduces measles, which has an infection rate of k = 0.25. Also suppose that the model for spread of an epidemic described in Example 3 applies.
(a) Write an equation for the number of natives who remain uninfected. Let t represent time in days.
(b) How many are uninfected after 30 days?
(c) How many are uninfected after 50 days?
(d) When will the maximum infection rate occur?