How do I add horizontal, vertical, diagonal and curved edges in this Tikz diagram?

Question

How do I draw this picture using Tikz?

A MWE using Zarko's solution found here Drawing the following diagram? :

    \documentclass[12pt, a4paper]{report}
\usepackage{tikz}
\usetikzlibrary{arrows.meta, positioning, quotes}

\begin{document}
   \begin{figure} \centering
  \begin{tikzpicture}[
node distance = 33mm and 33mm,
     N/.style = {draw, minimum size=12mm, inner sep=0pt},
            > = {Stealth[scale=0.6]},
 every edge/.append style = {draw, ->},
every edge quotes/.append style = {font=\small\linespread{0.75}\selectfont,
                                   inner sep=5pt, sloped}
                        ]
\node [N] (A) {$S$};
\node [N, right=of A] (B) {$A$};
\node [N,below=of B] (C) {$I$};
\node [N,left=of C] (D) {$R$};
%
\draw [<-] (A) -- ++(-1,0) node[left] {$b\left(1-\nu\right)$};
\draw [<-] (D) -- ++(-1,0) node[left] {$b\nu$};
\draw [->] (A) -- ++(0,1) node[above] {$\mu S$};
\draw [->] (B) -- ++(0,1) node[above] {$\mu A$};
\draw [->] ([xshift=-3.5mm] C.south) -- ++(0,-0.4) node[below] {$\alpha I$};
\draw [->] ([xshift=+3.5mm] C.south) -- ++(0,-0.4) node[below] {$\mu I$};
\draw [->] (D) -- ++(0,-1) node[below] {$\mu R$};
\draw[->] (B)--(D) node[midway,sloped,above]{$\gamma_A$};
%
\end{tikzpicture}
\setlength{\textfloatsep}{10pt plus 1.0pt minus 2.0pt}
\caption{Flow diagram for the SAIRS model.}
\end{figure}
    \end{document}

Feel free to improve on this MWE.

Answer 1

Here is a solution with tikz-cd and circledsteps:

    \documentclass[pdf]{article}
    \usepackage{mathtools}
    \usepackage{tikz-cd, circledsteps}
\begin{document}

\[ \begin{tikzcd}[column sep=large, row sep=large]
 & \mu & \mu \\
\arrow[r, "b(1-\nu)"] &\Circled{S} \arrow[r, "(\beta_AA + \beta_I I)"] \arrow[u]\arrow[d, shift right=0.75ex, "\rho", swap]& \Circled{A} \arrow[u]\arrow[ld, "\delta u", swap] \arrow[d, "\nu"]\\%
\arrow[r, "b\nu"] &\Circled{R}\arrow[d]\arrow[u, shift right=0.75ex, "\epsilon", swap] & \Circled{I}\arrow[l, "\delta_I", swap]\arrow[d] \arrow[l, bend left, "\tau"]\\
& \mu & \mu + \alpha
\end{tikzcd}
\]

\end{document}

Answer 2

Do you think about this plain TikZ code? Please update a more clearly hand-drawing ^^ PS: I will finish the diagram later.

\documentclass[12pt, a4paper]{report}
\usepackage{tikz}
\begin{document}
\begin{figure} 
\centering
\begin{tikzpicture}[>=stealth,thick]
\def\a{4}
\path[nodes={circle,draw,minimum size=12mm}]
(0,0)   node[fill=yellow] (R) {$R$}
(\a,0)  node[fill=red]    (I) {$I$}
(\a,\a) node[fill=cyan]   (A) {$A$}
(0,\a)  node[fill=green]  (S) {$S$}
;
\draw[->] (A)--(R) node[midway,sloped,above]{$\delta_a$};
\draw[->] (I)--(R) node[midway,above]{$\delta_I$};
\draw[->] (I.-135) to[bend left] node[midway,below]{$\tau$} (R.-45);
\draw[->] (S)--+(0,1.5) node[above]{$\mu$};
\draw[<-] (S)--+(-2,0) node[above]{$b(1-\mu)$};
\end{tikzpicture}
\caption{Flow diagram for the SAIRS model.}
\end{figure}
\end{document}