Indian immigrants are all over the world, so I don't find it weird to have people visiting your website from random countries ;)
Besides that - it might be perfectly correct. Imagine a scenario where someone just has this website opened in a tab (along with few dozens of other sites) and simply forgot about it while working on some other stuff.
That's how I work quite often - right now my Firefox got ~30 tabs opened, I use roughly 10 of them, some of tabs I have got running weren't closed since 2 days or more, because I plan to get back to them, but don't have time for it now. So all of the owners for sites I got running see exactly what you do: That someone from one location visits a website constantly with almost no activity. Now, due to the setting on a browser it might be possible that each tab is tracked as separate visitor, but... all of them are from one location.
I know it's rather a cruel way of twisting the GA results ;) but that's just how some people work :)