You should have no problem finding infectious diseases in Osaka...

Seriously - Osaka is a very big city and there will surely be university hospitals working in your field. I am almost sure of it. Also Takeda Pharmaceutical is Japan's largest pharma company - and they have their HQ in Osaka. Quite a lot of information is available in English for that company...

If you're trying to arrange an internship, I think your best bet is to get an introduction from someone who knows someone ... Basically you're asking the company to take some risk and expend some effort to have you on their campus for 6 weeks. Even if they don't have to pay you, they won't necessarily see the benefit.

Perhaps you have a teacher / professor from your school who would seek connections at the institutions?

Failing that, I would suggest trying to establish a connection through some kind of international business association / chamber of commerce / rotarians club / or similar association. If you are an Italian citizen then perhaps your embassy has some chamber of commerce type of organization?
(You may find that some of these organizations are mandated with "making Osaka business more international" or "promoting collaboration with Italy" - and that makes them more amenable to your approach).

There are some examples of the kinds of organizations that I am thinking of on the following page:
http://www.moveandstay.com/osaka/gui...g_business.asp

In my student days, I was fortunate to particpate in an internship with a manufacturing company here - the whole thing was arranged by the Shizuoka International Business Association. I don't think the manufacturing company would have given me the time of day if I had tried to contact them directly.