In a statement he shared on social media, Mr Bristow has addressed the concern about Covid-19 infection levels, but has said that some people on social media are using the pandemic as an "excuse to knock our city".
He noted that Peterborough currently has one of the highest infection rates in the country, but added: "Infection levels are coming down. Just a bit more slowly than some other parts of the country."
Mr Bristow addressed this by adding that Peterborough is a working city with many jobs that can't be done from home, with lots of key workers; while noting that our vaccine rollout in the city is "among the best in the country".
He added: "Other than right at the start of the pandemic, and when the new variant was identified, the city has consistently had infection levels below the UK average.
"We are a densely populated city with many of us living in the city centre and beyond living in HMO (houses of multiple occupants) and flats."
In a note to those who are looking on the city negatively, he continued: "I am sick to death of people knocking Peterborough and those who might be struggling. For so many lockdown is misery. They don’t have big houses, gardens, a well paid job that can be done from home, and a happy family.
"Let’s show compassion and understanding.
"Peterborough is a super city. Hopefully the end is in sight. Let’s stick to the rules for a little while longer. We will get through this together, #proudofpeterborough."
In the East of England, the regional R rate had dropped to between 0.6 and 0.8, slightly lower than the UK R rate which is between 0.6 and 0.9, though the East of England has one of the lowest rates in the country.
Across Peterborough and Cambridgeshire, more than 200,000 people have been given the first dose of the Covid-19 vaccine, which is 29% of the county's population.