Warwick is currently a champion that is fun to play but difficult to itemize. Many people would say Warwick is outclassed by many other junglers but with the right items you can slash them away. This build focuses Warwick as a jungle bruiser.

Pros
High Sustain
Can shred tanks with Hungering Strike
AoE buff with Hunters Call
Can secure kills with Blood Scent
Suppression with Infinite Duress

Cons
Extremely item dependent
Infinite Duress can be canceled by CC
No strong escape
Pre 6 Ganks are very weak.

Eternal Thirst - Passive
Think of this skill as sustain for early game and then at mid-late game, damage.

Hungering Strike - Q
This is your main source of damage. This can shred tanks and take a chunk out of carries. I personally keep this skill hot keyed so its easier on my mechanics. This skill resets your auto attack which is also handy to max out the eternal thirst passive in fights.

Hunters Call - W
totally useless on Warwick until late game where your team is trying to push down turrets fast. Until late game, your auto attack damage shouldn't be destructive so there really isn't a point to prioritize this skill.

Blood Scent- E
I like to max this skill out next because it secures your kills in ganks and gives you map awareness of low champions in teamfights trying to find a moment to flank our carries out. When not in use, it's dead weight. However in ganks, after you pop your ult and smash then, they should be bellow 50% health which let's you immediately chase down that enemy with no hope of escape.

Infinite Duress - R
The reason why warwick is feared in teamfights. The reason why I don't build pure AP on Warwick is because of this skill. Procs all on hit abilities and by the time you have all items. Try to survive 220 magic damage at full build plus 1 percent of the targets current HP every 0.33 seconds. At late game you will be feared and with your CDR, this skill will be spamable!

This build of Warwick is slightly different. I choose to run 21-0-9 on Warwick for a strong damage output and versatility.

I've tried regular AP 21 offensive mysteries but it's not as efficient as the one I use.
I've tried 21 on the defensive line and your damage gets nerfed hard if you do so. You already get strong sustain with Spirit Visage by mid-late game and your passive covers you early game so there really isn't any point in going full tank Warwick. Other jungle tanks can function better than a jungle tank Warwick.
21 on Utility is okay, but you have to finish the game fast. You need the EXP mastery so you can rush out your ultimate for stronger ganks which means you need to push those towers asap. It also gives you sustain, but the items can cover up Warwick in this department.


Offensive
Fury 4/4 Base attack speed helps you clear out your camps early level.
Butcher 2/2 Cost efficient way to clear our camps.
Destruction 1/1 Because this is AP Warwick, your damage output to structures is minimal and getting that extra damage on turrets can make a big impact on him since you will have a ton of AS on Warwick.
Havoc 3/3 Because your AP stats will be low, anything that will increase your damage by percentage is welcomed.
Blast 4/4 I personally don't like this mastery skill but it lets you unlock magic penetration.
Arcane Knowledge 1/1 Warwick needs magic penetration because your AP will be low, you need it.
Spellsword 1/1 boosts your damage output late game by a few points. It synergies with your AS stats and Infinite Duress.
Archmage 4/4 Percentages again. I cannot emphasis this enough! Because his base stats will be low, getting that extra AP will be helpful.
Executioner 1/1 needed to increase damage for weaker targets. You will know when this mastery will proc because Blood Scent will alert you the champions bellow 50% health.

Utility
Summoner's Insight 1/1 reduces Flash time. Gives you most escape on Warwick.
Meditation 3/3 Because we won't have any major mana items, getting something that will let you sustain your mana just by a bit will be very beneficial.
Improved Recall 1/1 This mastery helps when you are in tight situations.
Mastermind 3/3 Reduces both Flash and Smite cool downs which provides availability.
Runic Affinity 1/1 When you have the blue buff, this will let you hold on to it even longer so you won't have to worry about mana control.

You would wan't to open with the standard Hunter's Machete and 5 Health Potion.
At early game, your goals is to provide lane pressure relief and farm our way to level 6. Once you hit level 6 you can be way more aggressive with your gank until then just focus on camp farms. Spirit Stone will help you sustain your jungle for extended periods of time. Rushing Ninja Tabi and Wit's End lets you create a mix of defensive and offensive stats which are helpful in ganking lanes.

Once you hit mid game, you should focus on getting Spirit Visage. This item lets you sustain your self in team fights and you will also benefit from health and cool down reduction.

At this point in itemization you have 3 options that each fit in different scenarios.
Sunfire Aegis against ad champs that are rocking the game.
Liandry's Torment against tanks that are problematic to your team.
Nashor's Tooth to shut down carries fast with Infinite Duress.
When you are working to get your 6th item, you should sell your Spirit Stone.
Remember to get Elixir of Brilliance, Elixir of Fortitude and Oracle's Elixir for super sayain stats after you completed your build.

For enchantments if you are at the defensive take Enchantment: Homeguard. If you are on the offensive, take Enchantment: Alacrity.

In early game, focus on farming and relieving lane pressure until you hit level 6. If you want to be more aggressive, focus on counter jungling then and try to scrap up some duels if possible. Your sustain should win you in most cases.

Start at bottom buff and get a hard leash from your teammates. Go up to the upper buff and take that buff with smite then start deciding to farm or counter jungle. If the enemy jungler isn't a strong jungler. I prefer to counter jungle and try to scrap up kills.

Once you hit level 6, you can function more like an aggressive jungler. You should gank whenever your ult is up and when its down, farm or counter jungle.

Once your team starts teamfights, always wait for the first wave of CC to get used then ult the squishy carries so the enemy team will lose damage. That's your biggest goal when you play Warwick.

Remember to pop Hunters Call in teamfights! That buff will help out your team greatly!