The actress, 62, said she had already lost her grandmother and godmother to the virus.
She added that her sister Kelly, who has lupus, is now “fighting for her life” in the same hospital ward where her husband is also getting treatment for Covid-19.
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She urged people to vote for Democrat candidate Joe Biden and his vice presidential pick Kamala Harris.
Stone added that “with women in power we will fight for our families, we will fight for people to live and we will fight for people to get tested”.
She previously revealed on Sunday that her sister was in hospital with the virus as she urged people to wear face masks.