adding .Tex version of hands-out file

learners/files/hands-on.tex

@@ -0,0 +1,150 @@
+\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{Intrdocution}
+This document 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{3cm}}.
+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{3cm}}. 
+
+    The rate that explains the transition from  (\( E \)) to  (\( R \)) is the rate of \underline{\hspace{6cm}}.
+
+    \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. 
+
+\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 + \sigma)} \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 $\sigma = \frac{1}{10}$ (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}

renv/activate.R

@@ -98,6 +98,66 @@ local({
     unloadNamespace("renv")
 
   # load bootstrap tools   
+  ansify <- function(text) {
+    if (renv_ansify_enabled())
+      renv_ansify_enhanced(text)
+    else
+      renv_ansify_default(text)
+  }
+
+  renv_ansify_enabled <- function() {
+
+    override <- Sys.getenv("RENV_ANSIFY_ENABLED", unset = NA)
+    if (!is.na(override))
+      return(as.logical(override))
+
+    pane <- Sys.getenv("RSTUDIO_CHILD_PROCESS_PANE", unset = NA)
+    if (identical(pane, "build"))
+      return(FALSE)
+
+    testthat <- Sys.getenv("TESTTHAT", unset = "false")
+    if (tolower(testthat) %in% "true")
+      return(FALSE)
+
+    iderun <- Sys.getenv("R_CLI_HAS_HYPERLINK_IDE_RUN", unset = "false")
+    if (tolower(iderun) %in% "false")
+      return(FALSE)
+
+    TRUE
+
+  }
+
+  renv_ansify_default <- function(text) {
+    text
+  }
+
+  renv_ansify_enhanced <- function(text) {
+
+    # R help links
+    pattern <- "`\\?(renv::(?:[^`])+)`"
+    replacement <- "`\033]8;;ide:help:\\1\a?\\1\033]8;;\a`"
+    text <- gsub(pattern, replacement, text, perl = TRUE)
+
+    # runnable code
+    pattern <- "`(renv::(?:[^`])+)`"
+    replacement <- "`\033]8;;ide:run:\\1\a\\1\033]8;;\a`"
+    text <- gsub(pattern, replacement, text, perl = TRUE)
+
+    # return ansified text
+    text
+
+  }
+
+  renv_ansify_init <- function() {
+
+    envir <- renv_envir_self()
+    if (renv_ansify_enabled())
+      assign("ansify", renv_ansify_enhanced, envir = envir)
+    else
+      assign("ansify", renv_ansify_default, envir = envir)
+
+  }
+
   `%||%` <- function(x, y) {
     if (is.null(x)) y else x
   }
@@ -142,7 +202,10 @@ local({
     # compute common indent
     indent <- regexpr("[^[:space:]]", lines)
     common <- min(setdiff(indent, -1L)) - leave
-    paste(substring(lines, common), collapse = "\n")
+    text <- paste(substring(lines, common), collapse = "\n")
+
+    # substitute in ANSI links for executable renv code
+    ansify(text)
 
   }
 
@@ -306,7 +369,11 @@ local({
     )
 
     if ("headers" %in% names(formals(utils::download.file)))
-      args$headers <- renv_bootstrap_download_custom_headers(url)
+    {
+      headers <- renv_bootstrap_download_custom_headers(url)
+      if (length(headers) && is.character(headers))
+        args$headers <- headers
+    }
 
     do.call(utils::download.file, args)
 
@@ -385,10 +452,22 @@ local({
     for (type in types) {
       for (repos in renv_bootstrap_repos()) {
 
+        # build arguments for utils::available.packages() call
+        args <- list(type = type, repos = repos)
+
+        # add custom headers if available -- note that
+        # utils::available.packages() will pass this to download.file()
+        if ("headers" %in% names(formals(utils::download.file)))
+        {
+          headers <- renv_bootstrap_download_custom_headers(url)
+          if (length(headers) && is.character(headers))
+            args$headers <- headers
+        }
+
         # retrieve package database
         db <- tryCatch(
           as.data.frame(
-            utils::available.packages(type = type, repos = repos),
+            do.call(utils::available.packages, args),
             stringsAsFactors = FALSE
           ),
           error = identity
@@ -470,23 +549,31 @@ local({
 
   }
 
+  renv_bootstrap_github_token <- function() {
+    for (envvar in c("GITHUB_TOKEN", "GITHUB_PAT", "GH_TOKEN")) {
+      envval <- Sys.getenv(envvar, unset = NA)
+      if (!is.na(envval))
+        return(envval)
+    }
+  }
+
   renv_bootstrap_download_github <- function(version) {
 
     enabled <- Sys.getenv("RENV_BOOTSTRAP_FROM_GITHUB", unset = "TRUE")
     if (!identical(enabled, "TRUE"))
       return(FALSE)
 
     # prepare download options
-    pat <- Sys.getenv("GITHUB_PAT")
-    if (nzchar(Sys.which("curl")) && nzchar(pat)) {
+    token <- renv_bootstrap_github_token()
+    if (nzchar(Sys.which("curl")) && nzchar(token)) {
       fmt <- "--location --fail --header \"Authorization: token %s\""
-      extra <- sprintf(fmt, pat)
+      extra <- sprintf(fmt, token)
       saved <- options("download.file.method", "download.file.extra")
       options(download.file.method = "curl", download.file.extra = extra)
       on.exit(do.call(base::options, saved), add = TRUE)
-    } else if (nzchar(Sys.which("wget")) && nzchar(pat)) {
+    } else if (nzchar(Sys.which("wget")) && nzchar(token)) {
       fmt <- "--header=\"Authorization: token %s\""
-      extra <- sprintf(fmt, pat)
+      extra <- sprintf(fmt, token)
       saved <- options("download.file.method", "download.file.extra")
       options(download.file.method = "wget", download.file.extra = extra)
       on.exit(do.call(base::options, saved), add = TRUE)