fix typo for latex expression

Author: avallecam

episodes/contact-matrices.Rmd

@@ -227,7 +227,7 @@ When simulating an epidemic, we often want to ensure that the average number of
 
 Rather than just using the raw number of contacts, we can instead normalise the contact matrix to make it easier to work in terms of $R_0$. In particular, we normalise the matrix by scaling it so that if we were to calculate the average number of secondary cases based on this normalised matrix, the result would be 1 (in mathematical terms, we are scaling the matrix so the largest eigenvalue is 1). This transformation scales the entries but preserves their relative values.
 
-In the case of the above model, we want to define $\beta  C_{i,j}$ so that the model has a specified valued of $R_0$. If the entry of the contact matrix $C[i,j]$ represents the contacts of population $i$ with $j$, it is equivalent to `contact_data$matrix[i,j]`, and the maximum eigenvalue of this matrix represents the typical magnitude of contacts, not typical magnitude of transmission. We must therefore normalise the matrix $C$ so the maximum eigenvalue is one; we call this matrix $C_normalised$. Because the rate of recovery is $\gamma$, individuals will be infectious on average for $1/\gamma$ days. So $\beta$ as a model input is calculated from $R_0$, the scaling factor and the value of $\gamma$  (i.e. mathematically we use the fact that the dominant eigenvalue of the matrix $R_0 \times C_{normalised}$ is equal to $\beta / \gamma$). 
+In the case of the above model, we want to define $\beta  C_{i,j}$ so that the model has a specified valued of $R_0$. If the entry of the contact matrix $C[i,j]$ represents the contacts of population $i$ with $j$, it is equivalent to `contact_data$matrix[i,j]`, and the maximum eigenvalue of this matrix represents the typical magnitude of contacts, not typical magnitude of transmission. We must therefore normalise the matrix $C$ so the maximum eigenvalue is one; we call this matrix $C_{normalised}$. Because the rate of recovery is $\gamma$, individuals will be infectious on average for $1/\gamma$ days. So $\beta$ as a model input is calculated from $R_0$, the scaling factor and the value of $\gamma$  (i.e. mathematically we use the fact that the dominant eigenvalue of the matrix $R_0 \times C_{normalised}$ is equal to $\beta / \gamma$). 
 
 ```{r}
 contact_matrix <- t(contact_data$matrix)