The LCK+ Seiberg-Witten equations

Question

The LCK+ equations are defined for four-manifolds:

$$d\omega +\theta \wedge \omega =0$$

$$d\theta_+=0$$

with $\omega \in \Lambda_+(M)$ and $\theta$ is the Lee form.

Can we define LCK+-SW invariants for the Seiberg-Witten equations with LCK+ metrics?