Include Romain's contact generation TeX code in Vic revision

docs/papers/covid_19/preprocess/mixing_matrix/contacts_extrapolation_vic.tex

@@ -0,0 +1,9 @@
+\subsection{Contact matrices construction}
+For each location $L$ (home, school, work, other locations) the age-specific contact matrix $\mathbf{C^L} = (c_{i,j}^L) \in \mathbb{R}_{+}^{16 \times 16}$ is defined such that $c_{i,j}^L$ is the average number of contacts that a typical individual aged $i$ has with individuals aged $j$. As there is no contact survey available for Australia that is complete across all age groups, the matrices $\mathbf{C^L}$ were obtained by extrapolating contact matrices from the United Kingdom, being a country included in the POLYMOD study in 2005 \cite{RN141}. The original matrices from the United Kingdom are denoted $\mathbf{Q^L} = (q_{i,j}^L) \in \mathbb{R}_{+}^{16 \times 16}$, where $q_{i,j}^L$ is defined using the same convention as for $c_{i,j}^L$. The matrices $\mathbf{Q^L}$ were extracted using the R package ``socialmixr'' (v 0.1.8) and then adjusted to account for age distribution differences between Victoria and the United Kingdom.
+
+Let $\pi_j$ denote the proportion of people aged $j$ in Victoria, and $\rho_j$ the proportion of people aged $j$ in the United Kingdom. The contact matrices $\mathbf{C^L}$ were obtained from:
+$$
+c_{i,j}^L = q_{i,j}^L \times \frac{\pi_j}{\rho_j} . 
+$$
+
+In sensitivity analysis, we replaced the United Kingdom with Belgium as the proxy country from which survey data were used for constructing Victoria's matrices. Belgium was chosen as the POLYMOD country with the closest similarity in age distribution of Australia and Belgium in 2005.

docs/papers/tex/covid_library.bib

@@ -449,6 +449,19 @@ @article{RN66
    type = {Journal Article}
 }
 
+@article{RN141,
+   author = {Mossong, Joël and Hens, Niel and Jit, Mark and Beutels, Philippe and Auranen, Kari and Mikolajczyk, Rafael and Massari, Marco and Salmaso, Stefania and Tomba, Gianpaolo Scalia and Wallinga, Jacco and Heijne, Janneke and Sadkowska-Todys, Malgorzata and Rosinska, Magdalena and Edmunds, W. John},
+   title = {Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases},
+   journal = {PLOS Medicine},
+   volume = {5},
+   number = {3},
+   pages = {e74},
+   DOI = {10.1371/journal.pmed.0050074},
+   url = {https://doi.org/10.1371/journal.pmed.0050074},
+   year = {2008},
+   type = {Journal Article}
+}
+
 @misc{RN58,
    volume = {2021},
    number = {15 June},

docs/papers/tex/vic_supplement.tex

@@ -7,6 +7,8 @@
 \usepackage{soul}  % For highlighting text
 \usepackage{floatrow}  % For changing default font in tables
 \usepackage[font={sf, it}]{caption}
+\usepackage{amsmath}
+\usepackage{amssymb}
 
 \floatsetup[table]{font=sf}
 
@@ -33,6 +35,7 @@
 % Methods
 \input{../covid_19/model_description.tex}
 \input{../covid_19/stratifications/agegroup.tex}
+\input{../covid_19/preprocess/mixing_matrix/contacts_extrapolation_vic.tex}
 \input{../covid_19/stratifications/clinical.tex}
 \input{../covid_19/preprocess/case_detection.tex}
 \input{../covid_19/stratifications/tracing.tex}