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Mathematical Modeling: Healthcare and Medicine
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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?
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A
$I(t) = \frac{N}{1 + e^{-\beta t}}$
💡 Explanation:
The general solution to the differential equation $\frac{dI}{dt} = \beta I (1 - \frac{I}{N})$ is $I(t) = \frac{N}{1 + e^{-\beta t}}$. This can be obtained by using the method of separation of variables.