Warwick is known for his easy path through the jungle, his passive keeps him allive and even if not he still has his hungering strike to gain some health back. You can start either blue or redbuff, you dont rely on a strong botlane pull.
If you start bluebuff, you can smite the frog and just let him reset instantly, the thornmail effect will make the bluebuff an easy job, even without pull on level 1.
Later you need to farm some camps to gain the onhit dmg of Devourer (Jungle item enhancment/ new lantern).

Early its a hard time with warwick, because the only cc you have is the redbuff and eventually smite if you have an expanded jungle item. From level 6 and upwards its as easy as it was hard before: smite + ult will be about 70% health instantly and the lanechamp can deal some extra dmg in that time so if you have stime and ult you mostly get a safe kill.

Warwick still is an outtaker as he was allways, but now he not just suppresses but also will kill the weaker champs -> the carrys with one easy combo as described above (smite; ult; q; botrk), so he basicly just removes one enemy champ from the game, because later the respawn time is ~ same as the cooldown of your ult and smite.

This style of full offense ultimate Warwick can be named as the so known "noob-killer", so in normal games and non high ranked games it's mostly a safe win because the enemys don't allways know how to put that wolf to a leash, so you can carry yourself up to lower platin ranks easily
and then if you go full tryhard even higher.
In higher ranks the enemys will propably know how to avoid you or safe themselves from you.