First, determine the source of the leak. Are you sure that it comes from the vent? Did you check the toilet properly? It might be any leaks occurred from the toilet. I doubt it is a toilet leak. Wipe the bathroom with a sponge and make it dry. Then patiently check the source of the leak. If it from the toilet tank, the check the bolts, valve, and flapper properly. If the water level is above the overflow tube, the problem may be with the inlet valve and ballcock. And the flapper damage results in the water leak into the toilet bowl.
If the leak is from a corner, place butyl tape sealer on the both sides of the corner. The flow seal can be used to prevent the leaks originated from roof vents. I think it is better to
hire any professional plumbers to check out the problem and fix. I don't welcome the DIY repair because I'm afraid might it cause any harm.