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\documentclass{simiode}

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% With this version of the tex file and the associated SIMIODE.cls file you can produce BOTH a Student Version and a Teacher Version of your modeling scenario or technique narrative.
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% Basically the Student Version contains the title STUDENT VERSION along with the NAME OF SCENARIO, with no abstract, no keywords, no tags, no author identifiers, and no COMMENTS section. The Student Version contains only the STATEMENT of the modeling scenario with appropriate figures, data, instructions, and perhaps a bibliography appropriate for student resourcing, but nothing in the bibliography which would "give away" the nature of the modeling scenario, etc.
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%The Teacher Version contains the material in the Student Version, namely the title NAME OF SCENARIO, now headed with   TEACHER VERSION, but also full author  identification, abstract, key words, tag words, and, following the STATEMENT, a section of COMMENTS which can be discussion of presentation  ideas, "solutions," techniques, etc.
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% Authors can prepare a full Teacher Version using the notions immediately below  to create a pdf for review (but in review please eliminate all information about the author as we use a double-blind referee system. Such information will be restored when accepted and published in SIMIODE at www.simiode.org.
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%***********   Toggle the following line to turn the teacher version on (1) or off (0). ***********
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\def\TeacherEdition{0} % Toggle this line's value.
\newcommand{\teacher}[1]{\ifnum\TeacherEdition=1 #1 \fi}
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% The \teacher{ } command wraps any text that will appear only in the teacher version of
% the document. See this file for examples. This has been done for you in the document below.   
% Rename the pdf after you compile each final version.
% This option was created  by Eric Sullivan, Carroll College, Helena MT.
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\usepackage{amsmath,amssymb}
\usepackage{color}
\usepackage{graphicx}
\usepackage{url}
%\usepackage{hyperref}

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\begin{document}

\newpage
% You only need to change the NAME OF SCENARIO in the next line and delete the footnote. See above for instructions on toggling from Teacher Version to Student Version.
\title{\ifnum\TeacherEdition=1 TEACHER VERSION  \else STUDENT VERSION \fi\\MEDICINE PILL}




\markboth{Medicinal Pill}{Medicinal Pill}






\author{Brian Winkel,
Director SIMIODE\\
Chardon OH 44024 12518 USA\\
BrianWinkel@simiode.org
}

\makeStitlePDFLaTex


\begin{abstract}
Administration of a medicinal pill in single and multiple doses is modeled.
\end{abstract}

\section*{SCENARIO DESCRIPTION}


A medicinal pill, e.g., decongestant or antihistamine, is swallowed by a patient and enters the Gastro-Intestinal Tract (GI-Tract), whereupon it dissolves and then diffuses into the Bloodstream. Finally, the medicine leaves the body through Kidney and Liver removal. See Figure~\ref{fig:1-086-MainDiagram}.


\begin{figure}[h!]
\begin{center}
\includegraphics[width=12.0cm]{1-086-MainDiagram.png}



\caption{\label{fig:1-086-MainDiagram} Overview of activity for medicinal pill.}
\end{center}
\end{figure}

We consider two instances:

\begin{itemize}
\item [(a)] Just one pill with  $P$ mg of the medicine is administered.
\item [(b)] A regimen of pills, one per hour, each with $P$ mg of the medicine is administered.
\end{itemize}

\subsection*{Activities}

\begin{enumerate}
\item For both (a) and (b) model the amount of medicine in both the GI-tract and the Bloodstream over time in hours.  Be sure to make your assumptions clear and relevant.
\item In both cases, describe the amount of medicine in each compartment (GI-Tract and Bloodstream) with a plot based one some numbers you think are reasonable from your understanding of taking medicine, e.g., a doctor says, ``Take one every four hours.''
\item Describe the long term behavior of the amount of medicine in each compartment (GI-Tract and Bloodstream).
\item Reflect on the reasonableness of your model results.
\end{enumerate}








\teacher{
\section*{NOTES FOR TEACHERS}

The essence of this Modeling Scenario comes from \cite{BarnedFulford2002} where it appears as a section of Chapter 2:  Compartment Models. There are two cases explored in the text, first the single pill dosage and second the case of a course of pills.

We offer an analyses in a Mathematica notebook 1-086-T-Mma-MedicinalPill-TeacherVersion.nb and a pdf version of the file, 1-086-T-Mma-MedicinalPill-TeacherVersion.pdf, for those who do not use Mathematica. The file is fully annotated, thus enabling transcription for other software.

 

\begin{thebibliography}{98}




\bibitem{BarnedFulford2002} Barnes, Belinda and Glenn R. Fulford. 2002. {\it Mathematical Modelling with Case Studies\/}. London:  Taylor \& Francis.  pp. 41-45, 57.


\end{thebibliography}
}

\end{document}



