Hello there Areadriene here, but you can call me Area.

I have been trying out synergies with items than don't normally see much play time in all the cookie cutter builds that everyone runs. I remembered how much fun it was to zip around the map with Hecarim in the good old days but he has been hamstrung with balance changes and item reworks. Now I have found my preferred chaser Warwick, the Uncaged Wrath of Zaun.

I'd like to give shout out to Singed for making this pooch the apex predator in the jungle. His passive attack and move speed boosts as well as his innate heals make him an ideal ganker and if you play to those strengths he can snowball very quickly.

The attack speed allows for greater total DPS and the extra movement speed gives Warwick the early game map presence to apply pressure to any lane at any time.

Finish your jungle item first to get more hits which give more heals with the innate.
Next you want to grab Serrated Dirk and follow up with getting Boots of Mobility to amp up your chasing.
Then finish Youmuu's Ghostblade and make use of the active to clear jungle camps faster or save it to reach champs out of position quicker.
Deadman's is up next for some armor and health not to mention it puts your speed into hyper drive.
Follow up with Edge of Night for MR and Dusk Blade of Draktharr to round out the speed build.

Taking W first gives the extra oopmh to finish off camps and champs.
Grab Q second for the heal to avoid having to buy potions.
Grabbing E at Lvl 3 lets you CC champs as they TRY to escape.
Maxing Q 1st will allow you to do more opening damage and heal more efficiently.
Always max W next to burn down champs faster.

Ghost is so much more fun to use than flash with this build. It allows you greater map presence by quickly reaching a team fight. You can save it as a way to peel or you can use it to chase down that unlucky soul who decided to poke you instead of running as soon as they saw you.

Smite is self explanatory, take it or you go splat repeatedly in the jungle.

Old Warwick was all about attack speed and the novelty of on-hit. Reworked Warwick has greater potential to chase and dive champs. By utilizing his new supernatural speed you can apply more pressure to lanes and keep it up all game without sacrificing time in the jungle since you can move around and clear camps faster as a result.

Pros
Extremely fast out of combat to increase map pressence
Shuts champs down with his Ult
Has a low CD damage and heal with his Q

Cons
Not as tanky as some other junglers
Can easily be counter jungled prior to Lvl 6 if they are aggressive
Only has Ghost to escape unless you waste your Ult

Fastest Start
If your mid lane is willing to leash Raptors it allows you to take advantage of extra xp from being a level lower than the camp. Then you came move onto Red Buff and follow it up with top side Scuttle Crab to hit level 3 quickly.

Normal Start
Start top side buff to allow bottom lane to have a short at the entire first wave of creeps.
The you can run to Gromp/Krugs for fewer targets.
Finish up top side with Raptors or Gromp and grab the scuttle if you can for vision.

This is the point where you back to upgrade your smite and then scan the lanes to see who needs help the most. If all lanes are doing well I usually pick the lane who has the lowest health enemy and gank them before they can back. If I succeed I help smack the turret a couple times. If I have to fall back I grab the bottom scuttle crab for vision.
If scuttle is taken then I grab bottom side buff or invade the enemy bottom buff.
After my first full clear of the camps I look for another gank and then I alternate ganks in between each full top and full bottom clear. If I see enemy jungler gank the opposite side of the map then I steal one of their camps to limit the advantage they get from a successful gank. This helps to keep them behind if they fail.
By mid game I don't usually need camps anymore since I have snowballed enough to farm kills. When I am down I focus getting buffs and drags every time they are up to contribute more in team fights and make up for lost ground.