In addition to starting broadly and narrowing down to your thesis, another common way to begin an essay of the sort you describe is to start with something opposite of what you're writing about, or, to rephrase and explain, to start with something similar yet different.
In your case, you could start with the traditional flu. If you know the history, symptoms, and treatment of traditional flue, you can start with them, then lead into the swine flu.
Another option is to start with the common cold. This would be particularly relevant, since people seem to struggle with the ability, or inability, to tell the difference. This is vital because a cold doesn't usually require a doctor's visit or hospitalization, while the swine flu might.
Starting with something similar yet different, can be a way to naturally introduce your topic and thesis.