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fix typo
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amanda-minter committed Jan 23, 2025
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Expand Up @@ -225,7 +225,7 @@ To estimate the number of new hospitalisations we use a method called convolutio
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### What is convolution?

If we want to know how people are admitted to hospital on day $t$, then we need to add up the number of people admitted on day $t$ but infected on day $t-1$, day $t-2$, day $t-3$ etc. We therefore need to sum over the distribution of delays from infection to admission. If $f_j$ is the probability an infected individual who will be hospitalised will be admitted to hospital $j$ days later, and $I_{t-j}$ is the number of individuals infected on day $t-j$, then the total admissions on day $t$ is equal to $sum_j I_{t-j} f_j$. This type of rolling calculation is known as a convolution (see this [Wolfram article](https://mathworld.wolfram.com/Convolution.html) for some mathematical detail). There are different methods to calculate convolutions, but we will use the built in R function `convolve()`to perform the summation efficiently from the number of infections and the delay distribution.
If we want to know how people are admitted to hospital on day $t$, then we need to add up the number of people admitted on day $t$ but infected on day $t-1$, day $t-2$, day $t-3$ etc. We therefore need to sum over the distribution of delays from infection to admission. If $f_j$ is the probability an infected individual who will be hospitalised will be admitted to hospital $j$ days later, and $I_{t-j}$ is the number of individuals infected on day $t-j$, then the total admissions on day $t$ is equal to $\sum_j I_{t-j} f_j$. This type of rolling calculation is known as a convolution (see this [Wolfram article](https://mathworld.wolfram.com/Convolution.html) for some mathematical detail). There are different methods to calculate convolutions, but we will use the built in R function `convolve()`to perform the summation efficiently from the number of infections and the delay distribution.

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