Biohazard

Talk to Jerico, who is in the building south of the Ardougne north bank.

Search the cupboard in Jerico's house for some bird feed.

Go to the outside eastern wall of Jerico's house and pick up a pigeon cage.

Go back across the river, west of the castle to the West Ardougne gate.

Use bird feed on the watchtower fence (the spears, highlighted in red on your minimap) where several Mourners are perched above.

Open the pigeon cage.

Go south along the wall and talk to Omart. Make sure to finish the dialogue

Go to the east side of Martha Rehnison's house, highlighted in the picture (do not enter the house), north-west of where you breached the wall.

Take the rotten apple on the east outside of the house.

Squeeze through the gap in the metal fence directly east of the rotten apple.

Use the rotten apple on the cauldron in front of you. Make sure you right click it, as the left click option is to eat it.

Go to Nurse Sarah's house in the corner, south-west of the church.

Search the box on the north side of the house to obtain a doctors' gown.

Equip the gown.

Go to the north-east corner of the city and enter the Mourner Headquarters.

Open the door to the west and go upstairs.

Open the door to the east and kill a Mourner to obtain a key that automatically goes into your inventory.

Use the key on the gate in front of you to get into the caged room.

You can dispose of the key now

Search the crates in the caged room to find the distillator.

Teleport back to the Ardougne lodestone.

Talk to Elena in a house just west of the East Ardougne north bank, across the river.

Without teleporting, go to a bank and deposit your plague sample. Teleporting with the plague sample in your inventory will destroy it, forcing you to retrieve another sample from Elena.

Go to Rimmington and retrieve the three vials and the plague sample from the bank there.

Enter the westernmost house in Rimmington and talk to the Chemist. (Do not mention that you have the sample or he will take it away from you, and you will be forced to go back to Elena to get a new one. Also, do not give the wrong vial as it will force you to go back and get new ones).

At the fire outside the house talk to Chancy.

Talk to Da Vinci.

Talk to Hops.

Make sure to bank sample before teleporting. You can quickly bank the sample by using Bank chest to the east.

Teleport to Varrock.

If you have not done so already, obtain a priest gown set (can be bought from the nearby Fancy Clothes Store).

Go to the bank and get the plague sample.

Go through the gate in the south-east corner of Varrock.

Talk to the 3 chemist's assistants at the Dancing Donkey Inn to get the vials back.

Equip the priest gown top and bottoms now.

Go to the building south-east of the pub and go inside.

Talk to Guidor, tell him you are sent by Elena, and give him the samples.

Go back to Ardougne and talk to Elena.

Go to Ardougne Castle, south of Elena's house, and climb either the stairs to the north or south.

Talk to King Lathas, who is in the middle chamber of the first floor of the castle.

Quest complete!