One Model for the Spread of an Epidemic Is That $80 \%$

One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of 2,000 inhabitants, 130 people have a disease at the beginning of the week and 1,100 have it at the end of the week. How long does it take for $80 \%$ of the population to be infected?