Question

one model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected peopel and the number of uninfected people. in an isolated town of 5000 inhabitants, 160 people have a disease at the beginning of the week and 1200 have it at the end of the week. how long does it take for 80% of the population to be infected? answer: 15days but i want to know how you do the problem