How do I position my image such that it's in the centre of the slide?

Question

What I'm trying to do over here is that I want to position my plot as shown in the second image below in the centre, covering the text behind it. However, after passing different position parameters in the square brackets, I'm still not able to position the plot in the centre. Could anyone help me out with this?

The following is the code I've used:

\documentclass[demo]{beamer}  % remove 'demo' option in real document
\usepackage{mathtools}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\begin{frame}
\item We divided the procedure of solving the system of ODE into two main parts:
\begin{enumerate}
\item Estimating values for the parameters $\alpha, \beta, \gamma$ using linear regression and the empirical data we have
\begin{itemize}
     \item Empirical data is provided in the form of an $n$-by-4 matrix with coefficients $(t,P,S,Q)$
\end{itemize}


    \item Finding the general solution to the system of ODE that accepts $\alpha, \beta, \gamma$ as its parameters
        \begin{itemize}
            \item Remove independent variable $t$ from first two ODE to get a new ODE in terms of $P$ and $S$
            \item $\frac{dP}{dS} = \frac{P(-\alpha S -\gamma)}{S(\alpha P - (\beta + \gamma))}$
            \item Final equation: $\alpha (P+S) - \beta + \gamma \ln{\abs{P}} + \gamma \ln{\abs{S}} + C (*)$
            \item Next, by summing all three ODE, we get: $\frac{(P+S+Q)}{dt} = -\gamma (P+S+Q)$
            \item Integrating both side: $(P+S+Q) = K $e$^{-\gamma t} (**)$
    \end{itemize}
\end{enumerate}

    \pause 

    \begin{figure}[t]
    \centering
    \includegraphics[width=8cm]{one}
    \caption{Plot of $P(t)$, $S(t)$ and $Q(t)$ against $t$}
    \label{fig:3}
    \end{figure}

\end{frame}
\end{document}

Answer 1

Disregarding that it's probably a bad idea (instead of drawing over an existing frame, why not make a new one?), you could abuse tikz for this (I used my own minimal document, but that shouldn't matter):

\documentclass{beamer}
\usepackage{tikz,lipsum}

\begin{document}
    \begin{frame}{Frame Title}
        \begin{itemize}\item\lipsum[1]\end{itemize}
        %
        \begin{tikzpicture}[remember picture,overlay]
            \node at (current page.center) {\includegraphics[width=5cm]{example-image}};
        \end{tikzpicture}
    \end{frame}
\end{document}