Hi my name is BlindKidNoThumbs, I am a 13 year old Warwick main who recently hit diamond on OCE with a 65 percent winrate. According to leauge of graphs I'm currently the 3rd highest Warwick OCE and i'm rank 310 in the world. I have been playing league for 5 years. I hope my guide helps you to learn Warwick and to climb. Below is my op.gg if any of you are interested. Add me on League of Legends if you want to ask me any questions.
https://www.leagueofgraphs.com/summoner/oce/BlindKidNoThumbs
https://oce.op.gg/summoner/champions/userName=BlindKidNoThumbs

Warwick can clear single target jungle camps easily.
Warwick has one of the best level 3 dueling in the jungle meaning you can invade the enemy jungle.
Warwick also is a great duelist and early game skirmisher.
Warwick is a simple champion which allows you to focus more on other things like pathing, vision, execution and tracking.
Warwick has very high map pressure with his movement speed on his W and Celerity letting him counter gank and participate in every fight.
Warwick has a lot of crowd control meaning he can lock important champs down in a fight like Lucian or Master Yi.
Warwick also has a lot of healing meaning that the enemy team will have to buy Executioner's Calling. If they don't buy Executioner's Calling he is unkillable mid-late game.
Warwick is a great champ below master as the enemy will not respect his invade or him being able to rush objectives quickly. Also a lot of lower elo players stay on low hp making it very easy for you to clean them up with your Blood Scent.
Another great thing about Warwick is his objective taking power. He can easily solo dragon at level 4 with Smite. He can also take rift herald quickly. Also learn to combo your Smite with Jaws of the Beast.

The best and most common path is to match them. If Lee Sin starts on his red start on your blue then do blue, gromp, red in any order. After that you want to invade one of his buffs and duel him or take his buff. The reason you want to do this. Is as long as you ban Olaf. Warwick has the strongest level 3 duel with double buffs. This is making good use of your early game power and you are putting the enemy jungle behind.
Another thing that separates me from other jungles is after you invade you want to gank. This lets you extend your lead and lets your team help you at scuttle. When you have done that contest the scuttle that the enemy jungle. Is going to and try and double scuttle the enemy jungle. However if the enemy laners have pressure and are coming it is not worth dieing for. On your first back always try and aim to finish your Tiamat and Boots. However if you can't try and take your single target camps like gromp and wolves. Gank lanes and apply pressure. If you cannot get yourself ahead try and get a hyper carry like Vayne ahead and peel for her.