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Unfortunately, you and your brother are dealing with the inefficiency of the justice system. Since they are lawfully holding him pursuant to a valid warrant, there really is no timeframe in which they have to act, although there are constitutional protections generally available that should help expedite things.
You should contact the Pulaski County Sheriff office and demand to speak with the Sheriff or his next in command. Be polite, but firm in addressing your brother's situation and ask all pertinent questions, such as how long he will be held, what is the process of extradition, how extradition actually takes place (who will be transferring him), etc. You should also demand that this take place as soon as is reasonably possible. Also contact the Pulaski County District Attorney's Office and ask to speak with the DA. Go through the same set of questions. You should then contact the county and court from which the warrant emanates in Ohio and inform them of the situation and ask for their assistance in getting your brother home. Be able to provide them contact numbers to your brother's place of containment.
The squeaky wheel gets the grease in these situations, but you must remember, as frustrating as it is, to be respectful to the parties involved. A little respect goes a long way with law enforcement officers and those in the judicial system.
I hope this helps.