The image of cities as cauldrons of contagion is a very old one. In the 19th century, rapid urbanisation was accompanied by literal squalor and waves of often lethal communicable disease. Life expectancy declined during the Industrial Revolution as cities' populations surged.

But in recent years, US cities could boast that the so-called urban penalty had been reversed. "If you want to live longer and healthier than the average American, then come to New York City," former mayor Michael Bloomberg declared. This advantage continued with his successor, Mr Bill de Blasio.

New York had an average life expectancy roughly 2½ years longer than the nation's in 2017, the most recent year for which data is available. This is good news, since most of humanity lives in cities, and in the United States, over half of the population lives in cities of one million residents or more.

And then the coronavirus arrived, and New York became a hot spot for Covid-19 cases and deaths. As stay-home advisories rolled out, many wealthy city residents fled to country houses, beaches and boats.

Connecting the dots between population density and viral transmission seems simple logic. New York, with a population of 8.6 million, is the only American megacity. It is also the US centre of the pandemic.

But everything we know so far about the coronavirus tells us that blaming density for disease is misguided.

New York City Health Department data indicates that Manhattan, the borough with the highest population density, was not the hardest hit. Deaths are concentrated in the less dense, more diverse outer boroughs. Citywide, black and Latino residents are experiencing mortality rates that are twice those of white city dwellers.

Then there is the rest of the world. While the coronavirus first exploded in Wuhan, a city of 11 million, many "hyperdense" cities in Asia have been able to contain their outbreaks. The virus appeared in Singapore (5.6 million residents), Seoul (9.8 million), Hong Kong (7.5 million) and Tokyo (9.3 million), cities close in size to New York, but with much lower recorded deaths.

California and Hawaii, for example, have high population density - but not the highest Covid-19 mortality rates of the states. Albany, Georgia, with a population under 80,000, has among the highest case rates in the US (many related to attending a funeral).

Cities, large and dense by definition, do not inevitably support explosive viral transmission. But factors that do seem to explain clusters of Covid-19 deaths in the US are household crowding, poverty, racialised economic segregation and participation in the workforce.

The patterns of Covid-19 by neighbourhood in New York City track historical redlining that some 80 years ago established a legacy of racial residential segregation.

Population density is not the same as household overcrowding.

The US census defines crowding as more than one person per room, excluding the kitchen and bathroom. That means a one-bedroom apartment occupied by four people is crowded.

In 2013, the Bronx had New York City's highest percentage of crowded households (12.4 per cent), followed by Brooklyn (10.3 per cent) and Queens (9.3 per cent). Manhattan and Staten Island had 5.4 per cent and 3.4 per cent crowding. (Nationally, 2 per cent of people live in crowded households.)

Why are there so many crowded households in New York, including in its less densely populated neighbourhoods?

The answer is simple: the high cost of housing. High rents are also a principal driver of homelessness, which during this epidemic has proved deadly. Covid-19 has shown how risky crowded settings like homeless shelters, jails, detention centres and nursing homes can be.

It is no surprise that public health and urban planning have common roots and missions, because the quality and availability of housing, public transport and green spaces are so tied to health.

But as we think about the blueprint and design of cities, it is also critically important to consider the lived experience of individuals and how they navigate their urban space.

Imagine a low-wage worker, who holds two jobs to support her family and pay the rent, who has to work during this pandemic because her job is "essential", who works when sick because she has no sick leave.

She travels on a crowded bus, puts off medical care because she lacks insurance, and then returns to an apartment crammed with young children and elderly family members. Maybe she fills in on the night shift as an aide at a nursing home.

This all conspires to make her especially vulnerable to the coronavirus - with the result that her household, her nursing home and her neighbours are all liable to become sick as well. In this scenario, "the city" is not to blame for the explosion in cases of Covid-19.

That disease is devastating cities like New York because of the structure of healthcare, the housing market and the labour market, not because of their density. The spread of the coronavirus didn't require cities - we have also seen small towns ravaged. Rather, cities were merely the front door, the first stop.

It's not that there are too many people in cities. It's that too many of their residents are poor, and many of them are members of the especially vulnerable black, Latino and Asian populations.

That's what underlies the erroneous idea that, for those who can, it might be best to get far away from those people who endure household crowding and its risks.

It's wrong for the "haves" to seek remote, isolated housing for at least two reasons.

First, Covid-19 will be with us for some time. It has reached all 50 states and the District of Columbia. It has reached the White House. It sped to virtually every country in a few short months. It could just as well make inroads in the vacation communities and remote outposts where the wealthy have sought refuge.

Next, when the affluent seek separate communities, it is not good for democracy or, in the long run, society's stability. The way to ensure both is instead to invest in affordable housing and safer workplaces.

There are lessons from history.

In the 19th century, recurring epidemics were tackled with public health measures, improved sanitation, building standards, and the introduction of sidewalks and parks. These investments made possible cities that could be optimal places for living.

The walkability of urban areas builds exercise into everyday life, improving physical and mental health. The large numbers of people mean a tax base that can support cultural institutions, world-class medical care, public transport and parks.

Denser living is more efficient, less wasteful and kinder to the environment. It makes possible the interactions of all types of people, across the many divides of our society.

Right now, people have to take great care in congregating with other people - because proximity carries risks. But cities can do many things to reduce those risks.

They can increase the frequency of buses and trains to reduce crowding. They can create more pedestrian spaces and room for walkers and bikers. Above all, they can build more affordable housing.

Cities will remain a destination for families wanting a better future, young people looking to start a new life and migrants fleeing terror. Cities' density underlies their wonder - the people, the bustle, the democratic impulse born from the mixing of cultures and identities. They're also healthy places to live. Don't give up on them.

NYTIMES

• Mary T. Bassett directs the Francois-Xavier Bagnoud Centre for Health and Human Rights at Harvard University and was New York City's health commissioner from 2014 to 2018.