I know that when a famine occurs, there are no food or very little food and people starve to death. I do have one question, let say that an area was in a famine, why don't people find ways to escape? Like going to another area/country?

Part of it may be they don't want to leave their homes... perhaps where their families have lived for generations. It will also be an issue of how do they get somewhere else? How do they afford the costs of travel? By what means?

Lastly, how many countries do you know of that will welcome an influx of foreigners, with likely little means to support themselves, with open arms? Most countries would much rather send aid and humanitarian relief, if they can afford to in the first place, because most have an overburdened support system as it is... and issues with trying to help their own citizens in need... many of whom resent the support going to immigrants.

There is also the matter of money.

For instance if you are in Niger and you happen to go through a famine and you want to leave for US. 1 USD is like $140 so the hundred dollars it costs for the application is in USD that's a lot of cash.