Do airline companies have a Chief Medical Officer?
I'm not sure if every airline is the same. However each major airline I am familiar with does have a medical unit, usually headed by a doctor.

However, most of their efforts are actually dedicated internally - by that I mean looking after their employees. Things like:


Assessing the employees ability to return to work after an injury or illness
Fatigue management policy
Assessing whether a certain condition is acceptable to work with
Overseeing drug and alcohol rehabilitation (in some cases in Australia at least the employee is not automatically fired for being drunk/on drugs, they are allowed to complete a program and continue work)
Occupational health and safety assessments
General 'doctoring' duties for aircrew


Of course they are also involved in passenger health policy development, but as I said - the majority of their work is dealing with their own staff (at least, this is from my viewpoint, but I may not be seeing the whole picture). 

In terms of an outbreak like you have mentioned, there is always an action plan ready to be put in place which is developed with the government health department (or CDC in USA).