One Model for the Spread of an Epidemic Is That $5000$

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 $5000$ inhabitants, $130$ people have a disease at the beginning of the week and $1500$ have it at the end of the week. How long does it take for $50 \%$ of the population to be infected?

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