How much money in USD is needed for filing the invention patent internationally? What is the range of the cost?

A complete answer is much too complex at this point. It is very expensive to file for patents in other countries because you must file in each country that you want a patent - there is no "international" patent. There are treaties that allow certain filings that delay the time you have to file in each country for up to 30 months, but ultimately you will have to pay filing fees and attorneys fees in each country, plus you may have to get translations made. To file under the Patent Cooperation Treaty which can "save your filing date" for up to 30 months, you are looking at a minimum filing fee of over $2000.00 plus attorneys fees to prepare the application and drawings. The only sponsorship that is available is if you have investors - the government does not have any programs to sponsor inventors to file for patents. You need to talk to a patent attorney before you disclose your idea to anyone.