From bdbc25a11ea3d21ac4ee36b035a3c213eb59e6b1 Mon Sep 17 00:00:00 2001 From: Abdoelnaser M Degoot Date: Wed, 20 Nov 2024 21:07:24 +0000 Subject: [PATCH] adding .Tex version of hands-out file (#56) * adding .Tex version of hands-out file * add more questions * Update learners/files/hands-on.tex Co-authored-by: Andree Valle Campos * Update learners/files/hands-on.tex Co-authored-by: Andree Valle Campos * Update learners/files/hands-on.tex Co-authored-by: Andree Valle Campos * Update learners/files/hands-on.tex Co-authored-by: Andree Valle Campos * Update learners/files/hands-on.tex Co-authored-by: Andree Valle Campos * Update learners/files/hands-on.tex Co-authored-by: Andree Valle Campos * Update learners/files/hands-on.tex Co-authored-by: Andree Valle Campos * Update learners/files/hands-on.tex Co-authored-by: Andree Valle Campos * Update learners/files/hands-on.tex Co-authored-by: Andree Valle Campos * Update learners/files/hands-on.tex Co-authored-by: Andree Valle Campos --------- Co-authored-by: Andree Valle Campos --- learners/files/hands-on.tex | 159 ++++++++++++++++++++ renv/profiles/lesson-requirements/renv.lock | 138 ++++++++--------- 2 files changed, 230 insertions(+), 67 deletions(-) create mode 100644 learners/files/hands-on.tex diff --git a/learners/files/hands-on.tex b/learners/files/hands-on.tex new file mode 100644 index 00000000..c04a34a6 --- /dev/null +++ b/learners/files/hands-on.tex @@ -0,0 +1,159 @@ +\documentclass{article} +\usepackage{fancyhdr} + +% Set up the custom footer +\pagestyle{fancy} +\fancyfoot[R]{\thepage} % Centered page number in footer +\fancyfoot[C]{\textbf{License:} CC-BY.\textbf{Copyright:} Andree \& Degoot, 2024 } +\usepackage{tikz} +\usetikzlibrary{arrows.meta, positioning} +\usepackage{amsmath} +\author{Andree Valle Campos and Abdoelnaser M Degoot \\ Epiverse-TRACE Team @ LSHTM } +\title{Simple Introduction to Mathematical Modelling of Infectious Diseases} +\begin{document} +\maketitle + +\section{Introduction} +This practical aims to assess your understanding of the fundamental +principles of mathematical modeling while guiding you in constructing models using +a simple SEIR framework for infectious disease outbreaks.\\ + + \textbf{Note: Please fill in the blanks.} + +\section{SEIR Model} + + In the SEIR model, we have four compartments (\( S \), \( E \), \( I \), \( R \)): + +\begin{itemize} + \item \( S \) stands for \underline{\hspace{2cm}}, meaning \underline{\hspace{6cm}}. +The parameter that explains the transition from (\( S \)) compartment +to (\( E \)) compartment is \underline{\hspace{6cm}}. +\item \(E\) stands for \underline{\hspace{2cm}}, meaning that it can + \underline{\hspace{4cm}}. + + The rate that explains the transition from (\( E \)) to (\( I \)) is the rate of \underline{\hspace{1cm}}. + + \item \( I \) stands for \underline{\hspace{2cm}}, meaning that it can + \underline{\hspace{3cm}}. + The rate that explains the transition from (\( I \)) to (\( R \)) is the rate of \underline{\hspace{6cm}}. + + \item \( R \) stands for \underline{\hspace{3cm}}. This compartment includes those who have ceased to be infectious and acquire immunity against infection, regardless of the clinical course. +\end{itemize} + +\section{\( R_0 \)} +\( R_0 \) helps project the potential +size of an epidemic and calculate the herd immunity threshold. +It is defined as the average number of \underline{\hspace{2cm}} secondary cases +generated from a primary case in a completely +\underline{\hspace{3cm}} population. + +\section{\( R_t \)} +\( R_t \) +helps monitor the progress of the epidemic +When the population is no longer \underline{\hspace{2cm}}, the instantaneous +reproduction number \( R_t \) is used. This is defined as the average number +of s\underline{\hspace{2cm}} in a population composed of +\underline{\hspace{2cm}} and non-\underline{\hspace{2cm}} individuals at time \( t \). + +\section{A Diagram for Measles outbreak} + +Below is a typical SEIR model with demography (births and deaths). This is a simple +model applicable to person-to-person infections in a homogeneously mixing population. +Please carefully observe the model and examine the interactions with the equations +in section \ref{eqs}. Use color codes or arrows to relate the diagram to the equations. + + +\begin{center} + \begin{tikzpicture}[ + node distance=2cm, + every node/.style={fill=blue!10, draw, minimum size=1cm, text centered}, + arrow/.style={-Stealth, thick} + ] + + % Nodes + \node [circle, fill=green!75](S) {$S$}; + \node [circle, fill=orange!75](E) [right=of S] { $E$}; + \node [circle, fill=red!75](I) [right=of E] {$I$}; + \node [circle, fill=blue!75](R) [right=of I] {$R$}; + + % Arrows for transitions + \draw[arrow] (S) -- node[above, draw=none] {$\beta S \frac{I}{N}$} (E); + \draw[arrow] (E) -- node[above, draw=none] {$\sigma E$} (I); + \draw[arrow] (I) -- node[above, draw=none] {$\gamma I$} (R); + + % Natural birth and death rates + \draw[arrow] (-2,0.0) -- node[above, draw=none] {$\Lambda N$} (S); + \draw[arrow] (S) -- +(0,-1.2) node[below, draw=none] {$\mu$}; + \draw[arrow] (E) -- +(0,-1.2) node[below, draw=none] {$\mu$ }; + \draw[arrow] (I) -- +(0,-1.2) node[below, draw=none] {$\mu$ }; + \draw[arrow] (R) -- +(0,-1.2) node[below, draw=none] {$\mu$}; + + \end{tikzpicture} +\end{center} + +Where: +\begin{itemize} + \item \( \beta \): Transmission rate + \item \( \sigma \): Rate of progression from exposed to infectious + \item \( \gamma \): Recovery rate + \item \( \mu \): Death rate (natural death rate) + \item \( N \): Total population size, \( N = S + E + I + R \). +\end{itemize} + + The parameter $\beta$ is derived from the multiplication of $p$ + and $c$, where $p$ is the probability of transmission during contact, and $c$ + is the contact rate, defined as the average number of contacts per unit of time.\\ + +Model parameters are often (but not always) specified as rates. +The rate at which an event occurs is the inverse of the average time until that event. +For example, in the SEIR model, the recovery rate $\gamma$ is the inverse of the average infectious period.\\ + +Values of these rates can be determined from the natural history of the disease. +For example, if people are on average infectious for 8 days, then in the model, +1/8 of currently infectious people would recover each day +(i.e. the rate of recovery, $\gamma=1/8=0.125$). + +\section{Equations}\label{eqs} +Note that in the diagram, arrows entering compartments are expressed as positive +terms in the equations, while arrows exiting compartments are represented with negative terms. +Based on the above diagram,deduce the following equations that describe this system: + +\section*{Compartment Equations} + +\begin{itemize} + \item \textbf{S compartment:} + \[ + \frac{dS}{dt} = + \] + + \item \textbf{E compartment:} + \[ + \frac{dE}{dt} = + \] + \item \textbf{I compartment:} + \[ + \frac{dI}{dt} = \ + \] + + \item \textbf{R compartment:} + \[ + \frac{dR}{dt} = + \] +\end{itemize} + +\section{Computing $R_0$} +The expression for the basic reproduction number ($R_0$) in the above system is given by: + +\begin{equation*} R_0 = \frac{\mu}{(\mu + \alpha)} \frac{\beta}{(\mu + \gamma)}. \end{equation*} + +To calculate the $R_0$ value for given parameter values, write an R function +called Measles$R_0$ that implements this formula. The function will use the following parameter values: + + \begin{itemize} + \item $\mu = \frac{1}{75}$ (natural mortality rate) + \item $\alpha = \frac{1}{10}$ (rate of progression from the exposed to the infectious stage) + \item $\gamma = 1/8$ (recovery rate) + \item $\beta = 1.8$ (transmission rate) + \end{itemize} +Then compute the final size of such epidemic. +\end{document} \ No newline at end of file diff --git a/renv/profiles/lesson-requirements/renv.lock b/renv/profiles/lesson-requirements/renv.lock index 865a53c3..afe33935 100644 --- a/renv/profiles/lesson-requirements/renv.lock +++ b/renv/profiles/lesson-requirements/renv.lock @@ -20,7 +20,7 @@ "Package": "DBI", "Version": "1.2.3", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "methods" @@ -91,7 +91,7 @@ "Package": "R6", "Version": "2.5.1", "Source": "Repository", - "Repository": "RSPM", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R" ], @@ -101,7 +101,7 @@ "Package": "RColorBrewer", "Version": "1.1-3", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R" ], @@ -135,7 +135,7 @@ "Package": "askpass", "Version": "1.2.0", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "sys" ], @@ -145,7 +145,7 @@ "Package": "backports", "Version": "1.5.0", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R" ], @@ -155,7 +155,7 @@ "Package": "base64enc", "Version": "0.1-3", "Source": "Repository", - "Repository": "RSPM", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R" ], @@ -189,7 +189,7 @@ "Package": "blob", "Version": "1.2.4", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "methods", "rlang", @@ -254,7 +254,7 @@ "Package": "callr", "Version": "3.7.6", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "R6", @@ -267,7 +267,7 @@ "Package": "cellranger", "Version": "1.1.0", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "rematch", @@ -302,7 +302,7 @@ "Package": "clipr", "Version": "0.8.0", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "utils" ], @@ -326,7 +326,7 @@ "Package": "conflicted", "Version": "1.2.0", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cli", @@ -392,7 +392,7 @@ "Package": "dbplyr", "Version": "2.5.0", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "DBI", "R", @@ -441,7 +441,7 @@ "Package": "dplyr", "Version": "1.1.4", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "R6", @@ -464,7 +464,7 @@ "Package": "dtplyr", "Version": "1.3.1", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cli", @@ -518,7 +518,7 @@ "Package": "fansi", "Version": "1.0.6", "Source": "Repository", - "Repository": "RSPM", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "grDevices", @@ -530,7 +530,7 @@ "Package": "farver", "Version": "2.1.2", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Hash": "680887028577f3fa2a81e410ed0d6e42" }, "fastmap": { @@ -558,7 +558,7 @@ "Package": "fontawesome", "Version": "0.5.2", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "htmltools", @@ -570,7 +570,7 @@ "Package": "forcats", "Version": "1.0.0", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cli", @@ -586,7 +586,7 @@ "Package": "fs", "Version": "1.6.4", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "methods" @@ -597,7 +597,7 @@ "Package": "gargle", "Version": "1.5.2", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cli", @@ -619,7 +619,7 @@ "Package": "generics", "Version": "0.1.3", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "methods" @@ -630,7 +630,7 @@ "Package": "ggplot2", "Version": "3.5.1", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "MASS", "R", @@ -655,7 +655,7 @@ "Package": "glue", "Version": "1.7.0", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "methods" @@ -666,7 +666,7 @@ "Package": "googledrive", "Version": "2.1.1", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cli", @@ -691,7 +691,7 @@ "Package": "googlesheets4", "Version": "1.1.1", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cellranger", @@ -719,7 +719,7 @@ "Package": "gtable", "Version": "0.3.5", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cli", @@ -734,7 +734,7 @@ "Package": "haven", "Version": "2.5.4", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cli", @@ -755,7 +755,7 @@ "Package": "highr", "Version": "0.11", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "xfun" @@ -766,7 +766,7 @@ "Package": "hms", "Version": "1.1.3", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "lifecycle", "methods", @@ -811,7 +811,7 @@ "Package": "httr", "Version": "1.4.7", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "R6", @@ -826,7 +826,7 @@ "Package": "ids", "Version": "1.0.1", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "openssl", "uuid" @@ -860,7 +860,7 @@ "Package": "isoband", "Version": "0.2.7", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "grid", "utils" @@ -871,7 +871,7 @@ "Package": "jquerylib", "Version": "0.1.4", "Source": "Repository", - "Repository": "RSPM", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "htmltools" ], @@ -907,7 +907,7 @@ "Package": "labeling", "Version": "0.4.3", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "graphics", "stats" @@ -933,7 +933,7 @@ "Package": "lifecycle", "Version": "1.0.4", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cli", @@ -946,7 +946,7 @@ "Package": "lubridate", "Version": "1.9.3", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "generics", @@ -959,7 +959,7 @@ "Package": "magrittr", "Version": "2.0.3", "Source": "Repository", - "Repository": "RSPM", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R" ], @@ -981,7 +981,7 @@ "Package": "memoise", "Version": "2.0.1", "Source": "Repository", - "Repository": "RSPM", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "cachem", "rlang" @@ -1009,7 +1009,7 @@ "Package": "mime", "Version": "0.12", "Source": "Repository", - "Repository": "RSPM", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "tools" ], @@ -1019,7 +1019,7 @@ "Package": "modelr", "Version": "0.1.11", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "broom", @@ -1037,7 +1037,7 @@ "Package": "munsell", "Version": "0.5.1", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "colorspace", "methods" @@ -1086,7 +1086,7 @@ "Package": "pillar", "Version": "1.9.0", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "cli", "fansi", @@ -1103,7 +1103,7 @@ "Package": "pkgconfig", "Version": "2.0.3", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "utils" ], @@ -1134,7 +1134,7 @@ "Package": "processx", "Version": "3.8.4", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "R6", @@ -1172,7 +1172,7 @@ "Package": "purrr", "Version": "1.0.2", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cli", @@ -1198,7 +1198,7 @@ "Package": "rappdirs", "Version": "0.3.3", "Source": "Repository", - "Repository": "RSPM", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R" ], @@ -1208,7 +1208,7 @@ "Package": "readr", "Version": "2.1.5", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "R6", @@ -1231,7 +1231,7 @@ "Package": "readxl", "Version": "1.4.3", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cellranger", @@ -1246,14 +1246,14 @@ "Package": "rematch", "Version": "2.0.0", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Hash": "cbff1b666c6fa6d21202f07e2318d4f1" }, "rematch2": { "Package": "rematch2", "Version": "2.1.2", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "tibble" ], @@ -1336,7 +1336,7 @@ "Package": "rvest", "Version": "1.0.4", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cli", @@ -1369,7 +1369,7 @@ "Package": "scales", "Version": "1.3.0", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "R6", @@ -1389,7 +1389,7 @@ "Package": "selectr", "Version": "0.4-2", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "R6", @@ -1438,7 +1438,7 @@ "Package": "stringi", "Version": "1.8.4", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "stats", @@ -1451,7 +1451,7 @@ "Package": "stringr", "Version": "1.5.1", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cli", @@ -1468,7 +1468,7 @@ "Package": "sys", "Version": "3.4.2", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Hash": "3a1be13d68d47a8cd0bfd74739ca1555" }, "systemfonts": { @@ -1476,6 +1476,10 @@ "Version": "1.1.0", "Source": "Repository", "Repository": "https://carpentries.r-universe.dev", + hands-out-pdf + "RemoteUrl": "https://github.com/r-lib/systemfonts", + "RemoteRef": "v1.1.0", + "RemoteSha": "78df90ca6d869feeb6a40c88f72269093505aa22", "Requirements": [ "R", "cpp11", @@ -1500,7 +1504,7 @@ "Package": "tibble", "Version": "3.2.1", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "fansi", @@ -1519,7 +1523,7 @@ "Package": "tidyr", "Version": "1.3.1", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cli", @@ -1542,7 +1546,7 @@ "Package": "tidyselect", "Version": "1.2.1", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cli", @@ -1558,7 +1562,7 @@ "Package": "tidyverse", "Version": "2.0.0", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "broom", @@ -1598,7 +1602,7 @@ "Package": "timechange", "Version": "0.3.0", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cpp11" @@ -1619,7 +1623,7 @@ "Package": "tzdb", "Version": "0.4.0", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cpp11" @@ -1630,7 +1634,7 @@ "Package": "utf8", "Version": "1.2.4", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R" ], @@ -1650,7 +1654,7 @@ "Package": "vctrs", "Version": "0.6.5", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cli", @@ -1664,7 +1668,7 @@ "Package": "viridisLite", "Version": "0.4.2", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R" ], @@ -1692,7 +1696,7 @@ "Package": "vroom", "Version": "1.6.5", "Source": "Repository", - "Repository": "CRAN", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "bit64", @@ -1766,7 +1770,7 @@ "Package": "xml2", "Version": "1.3.6", "Source": "Repository", - "Repository": "RSPM", + "Repository": "https://packagemanager.posit.co/all/__linux__/jammy/latest", "Requirements": [ "R", "cli",