$$
J =
\begin{pmatrix}
r - \frac{2rT^*}{\bar T} - \beta D^* & -\beta T^* & 0 \\[4pt]
\gamma D^* & \gamma T^* - E^* & -D^* \\[4pt]
0 & \alpha & -\mu
\end{pmatrix}
$$