In your own words;
Link: https://www.tacreports.org/storage/documents/treatment-behind-bars/treatment-behind-bars.pdf
This is a long report, but if you read the Executive Summary you will get a general overview of the problem of mentally ill in prisons and jails.
There also is a state by state summary of treatment for the mentally ill
1) Why are there so many mentally ill people in prisons and jails?
2) What treatment do they require?
3) What are some effective alternatives to incarceration for the mentally ill
4) Choose one state and explain what that state is doing to treat mentally ill inmates.