Answering this question will involve a bit of math...
The probability of a shiny by itself it 16 in 65,536 or 1 in 4,096.
The probability of a shiny with the Shiny Charm is 6 in 4,096.
The probability of getting a Pokemon with Pokerus is 3 in 65,536.
Time for the calculator.
N= No Shiny Charm
W= With Shiny Charm
16/65,536 as a decimal is 0.000244140625.
3/65,536 as a decimal is 0.046153846154.
6/4,096 as a decimal is 1.5.
N= 0.000244140625 X 0.046153846154 = 0.00001126802884619140625 = 0.00001126802884619140625
W= 1.5 X 0.04615384615 = 0.096230769225
The chance of catching a shiny Pokemon with Pokerus without the Shiny Charm is a 0.00001126802884619140625 chance.
The Chance of catching a shiny Pokemon with Pokerus with the Shiny Charm is a 0.096230769225 chance.
But wait! There's more!
The person who traded you the Latias could've just caught it shiny and spread Pokerus onto it. If you have a Pokemon in your party with Pokerus and different Pokemon without Pokerus it can spread onto the Pokemon without Pokerus.
The Latias is definitely very rare if the person who traded it to you caught it in the wild, even if he spread Pokerus to the Latias it is still rare. Or the person could've just hacked the Latias.
Hope I helped!