For either side to have been responsible for the virus would need some reason for the two worlds to have significant differences in the macro world for one side to have let the virus out and not the other. But the virus is itself is the cause of the sides being different in the macro world, not an effect. (If it were a result, we would have the loose end of the missing cause for the sides being different.) The mutation of a virus is (often) the result of the ionizing radiation that is the result of a quantum mechanical process, which reasonably would have differing outcomes on the two sides. For this reason I think the virus just happened, as viruses do, and Alpha was lucky while Prime was not.