How to build a multi-regional web application architecture?

My server is in Sweden (DB, ruby on rails web app, nginx). Sometimes people from South Africa and Southeast Asia come to my site.

For these people, the site is very stupid. Ping from Southeast Asia about 200ms. I want to solve this problem. I have no experience with such situations.

CDN will not help because it is only for static information.

I thought I need to make three servers for each region (1 server 1 nginx 1 webapp 1 base 1 region) and configure replication between databases. But I was told it was bad. How then? Maybe Amazon Cloud with RDS?