I would like to graph the following function, 10000/(9999*e^(-0.125*x)+1) using Tikz and PGFplots but I can not seem to get it to work. I would like labels for the horizontal axis (t) and the vertical axis (I). I want the range of the function to be from 0 to 10,000 so I could see the asymptote being reached over time. However I can't seem to figure out how to make the two axes go up to 10,000 without making the axes itself too big to fit on paper.
I have used this so far, but I would like the tick marks to read 0, 1000, 2000, or something similar, up to 10000. Moreover, I do not want it to use scientific notation for the tick marks. My graph seems not to look like as I want it as well.
\documentclass{amsart}
\usepackage{pgfplots}
\pgfplotsset{compat=1.8}
\usepackage{mathtools}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\begin{axis}[scaled ticks=false,xlabel=Time, ylabel=Infectious Individuals,xmin=0,ymin=0]
\addplot[domain=0:150, blue, ultra thick,smooth] {10000/(9099*e^(-0.125*x)+1)};
\end{axis}
\end{tikzpicture}
\end{document}
Edit -
I have been able to obtain - But I would like to draw an asymptote at 10000 as well as having the origin of the axis starting at 0,0 not as it is seen. Lastly, how would I go by adding labels for the axes?


\addplotline is different from the one in your question:(10000/(9999*e^(-0.125*x))+1)vs.10000/(9999*e^(-0.125*x)+1). – LucaD Dec 08 '15 at 17:13\begin{axis}[scaled ticks=false]– LucaD Dec 08 '15 at 17:220:100and you'll see the behavior of the function. – Herr K. Dec 08 '15 at 17:26xlabel=x axis, ylabel=y axisto theaxisenvironment for axis labels. You can also setxmin=0,ymin=0for the curve to start at(0,0)– Herr K. Dec 08 '15 at 17:32h!to thefigureenvironment, as in\begin{figure}[h!]. This influences the placement algorithm. See this post for more detail. – Herr K. Dec 08 '15 at 17:39