Several ways:

Cancel nothing and don't:
"There is something we see in our health inequalities that doesn't mirror (trends in) Alameda County, California, or the United States."

Cancel nothing and doesn't:
"There is something we don't see in our health inequalities that mirror (trands in) Alameda County, California, or the United States."

Cancel don't and doesn't:
"There is nothing we see in our helath inequalities that mirrors (trends in ) Alameda, County, California, or the United States."

I vote for option 3.
 

quad negative