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Mathematical Modeling: Healthcare and Medicine

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Multiple Choice

In a study of the spread of a contagious disease, the number of infected individuals is given by the differential equation $\frac{dI}{dt} = \beta I (1 - \frac{I}{N})$, where $\beta$ is the transmission rate, $I$ is the number of infected individuals, and $N$ is the total population. What is the general solution to this differential equation?

  1. $I(t) = N(1 - e^{-\beta t})$
  2. $I(t) = \frac{N}{1 + e^{-\beta t}}$
  3. $I(t) = \frac{N}{1 - e^{-\beta t}}$
  4. $I(t) = N e^{-\beta t}$
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