Jackson said inmates are trapped in what "amounts to graveyards."
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Jackson and Rev. Dr. Frederick D. Haynes, III, senior pastor of the Friendship Baptist Church in Dallas, launched a new nationwide initiative seeking the release of inmates vulnerable to COVID-19.
Dozens of religious and community leaders from across the country took part in a conference call about the initiative Saturday.
"How can those in jail be safely housed there?" Haynes asked. "How can jails be safe for those who are working there? We are also concerned about the adequacy of personal protection equipment, supplies, social distancing, etc."
Three Cook County Jail inmates have died after contracting COVID-19.
Cook County Sheriff Tom Dart has told ABC 7 that all proper precautions are being taken to keep staff and inmates safe. But attorneys for some prisoners said dangerous violations continue and they requesting more action to stop the spread of the virus.
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RELATED: Court order hasn't stopped COVID-19 spread at Cook County Jail; attorneys want drastic action
Rev. Jesse Jackson is among a growing chorus of medical professionals, activists and political figures pressuring the federal government to not just release comprehensive racial demographic data of the country's coronavirus victims, but also to outline clear strategies to blunt the devastation on African Americans and other communities of color.
This week, Jackson's Rainbow PUSH Coalition and the National Medical Association, a group representing African American physicians and patients, released a joint public health strategy calling for better COVID-19 testing and treatment data. The groups also urged officials to provide better protections for incarcerated populations and to recruit more African Americans to the medical field.
Jackson also expressed support for a national commission to study the black COVID-19 toll modeled after the Kerner Commission, which studied the root causes of race riots in African American communities in the 1960s and made policy recommendations to prevent future unrest.
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On Friday, the Centers for Disease Control and Prevention released its first breakdown of COVID-19 case data by race, showing that 30% of patients whose race was known were black. The federal data was missing racial information for 75% of all cases, however, and did not include any demographic breakdown of deaths.
The latest Associated Press analysis of available state and local data shows that nearly one-third of those who have died are African American, with black people representing about 14% of the population in the areas covered in the analysis.
In Chicago, deaths among the African-American community account for about 62% of COVID-19 deaths. The rate is down slightly from 72% reported earlier, but still far higher than any other group. African Americans also comprise 48% of city cases.
The Associated Press contributed to this report.