"My wife Aurora now rests in peace with God. She passed away today in the early morning of Sunday, July 19, 2020," he wrote.
"I have faith in God that she is with him and has moved on to a better life. We will forever miss her and remember her for the strong, loving and caring person she was."
The Esparzas already had a 7-year-daughter and a 1-year-old son.
Speaking to Fox 9 before her death, Duran said: "She is a 35-year-old healthy woman with no pre-existing conditions. We never thought this could happen to our family."
He said the reality of the situation hit home when he was advised by the doctors that a caesarean would be necessary.
"'That's when it hit me. I was thinking 'okay she's going to get through this, a few days at the hospital'. But when I received that phone call it just hit me."
After the birth, Esparza's health continued to decline and her husband lobbied for her to be moved to another hospital where she could receive extracorporeal membrane oxygenation (ECMO) treatment, which carries out the function of the heart and lungs outside of the body.
However, all his requests were denied.
North Memorial Hospital said in a statement to Fox 9 News: "North Memorial Health partners with local and regional healthcare systems to care for patients who would benefit from ECMO, which is a highly specialised service that is typically only offered at ECMO Centers."
"We do not offer ECMO as a long-term or ongoing treatment which would be required to treat Covid-19, but we do use it for short-term emergency care as part of our trauma and cardiovascular surgery programmes, when needed," they added.
"ECMO Centers have stringent criteria for accepting patient referrals and our medical teams work closely with these partners to ensure that our patients have access to the care they need."
Duran hopes that his wife's story helps others to realise the danger posed by Covid-19.
"Just be cautious because you could be healthy just like my wife and still end up in the ICU on the ventilator," he said.