There is some but limited evidence that large cities pose a greater risk of infectious diseases. As we will see beow, there is an elevated risk of measles when the city exceeds a critical population, and there is a greater risk of sexually transmitted diseases. There is little evidence for increased risks of other kinds of diseases.
Critical Community Size
The critical community size, an idea introduced by Bartlett (1957), refers to a threshold population size for a city with respect to the spread of an infectious disease. Below the critical community size, an infectious disease outbreak is more likely than not to dwindle and disappear until reintroduced from the outside. Above that critical size, the disease remains endemic indefinitely in the population. Bartlett (1960), based on measles data, estimates the critical community size to be around 250,000 to 300,000 people in the United States, with a fadeout time of two years for cities below the critical community size. However, Bartlett (1960) acknowledges that the concept of a critical community size may be losing relevance due to increased travel of people between cities.
To deal with the relative isolation of communities, Black (1966) examines up to 15 years of measles case reports in 19 island communities and finds that in all communities of less than 500,000 people, there were breaks in transmission. Black’s number is higher than Bartlett’s number in part because isolated islands have less opportunity to import the virus from outside (Keeling and Grenfell 1997. He concludes that measles could not have been sustained in pre-agricultural societies and must have developed after the diffusion of agriculture. It is now thought that measles is of zoonotic origin and diverged from the rinderpest virus that afflicts cattle around the 11th or 12th centuries; see Furuse, Suzuki, and Oshitani (2010).
Conlan and Grenfell (2007) provide a good theoretical basis for the spread of infectious disease and the critical community size. Their mathematical model is based on three assumptions. The first is frequency-dependent mass action mixing. This implies that each contact of two people has a certain probability of transmitting the disease. The other common mixing assumption is density-dependent, which depends on the city size or population density. Which assumption is more appropriate depends on the specifics of the disease, and Bjørnstad, Finkenstädt, and Grenfell (2002) show that the frequency-dependent model is appropriate for measles. The other assumptions are homogenous transmission rates with respect to age and discrete infectious periods.
It should be emphasized that the that the critical community size is probabilistic. For example, Bartlett (1960) define CCS as the point at which there is a 50% probability of the disease disappearing in two years. Therer is a possibility of the disease persisting in smaller communities or disappearing in larger communities. A “community” is typically defined as a region with a high degree of population mixing and is roughly equivalent to a metropolitan area rather than an administrative city. Additionally, population size is not the only important variable. Grunning and Wearing (2013) find, as intuition would suggest, that higher vaccination rates increase the critical communuity size, while higher birth rates decrease it.
Diseases Other than Measles
No other disease has had its epidemiology studied as well as measles, but looking at research related to city size and other infectious diseases helps round out our picture.
Metcalf et al. (2013) examine four diseases: measles, mumps, pertussis (whooping cough), and rubella. They find that the CCS for three of these diseases is similar, with the CCS for pertussis about a fifth of that of the others. Furthermore, they find that the probability of disappearance is about twice as much on islands communities as it is for mainland communities. Of the four diseases, mumps extinction is by far the most affected by a community’s island status, suggesting that mumps infections are highly dependent on reintroduction form the outside world.
Broutin, Simondon, and Guégan (2004) examine pertussis epidemiology in rural Senegal. They find no clear CCS threshold; if there is a threshold, each community they examine sits below that value. However, they do find evidence of CCS-like curves. This may be in part due to the differences between pertussis and measles. Unlike with measles, pertussis immunity wanes over time, though individuals are less contagious on infections after the first.
Diseases with Reservoirs
Measles is a particularly well-studied case, and it is also one where the critical community size model works well. For some other diseases, as we saw above, the CCS model is weaker. In some cases, it breaks down entirely.
For some diseases, infected individuals remains contagious, whether or not they show symptoms, for years or even for the rest of their lives. In that case, infected individuals act as an internal reservoir.
McQuillan et al. (2018) observes a decline in the herpes simplex virus, type 1 and 2 in the United States since 2000, with HSV-1 declining in other countries as well. In an interview, she attributes this to a reduction in crowding and improvement in hygiene. City size and population density likely matter only insofar as they affect these more direct variables.
Sexually transmitted diseases, the prevalence of which is obviously correlated with sexual activity, show more prevalence in urban areas and in large cities in particular. Bettencourt et al. (2007), a foundational work of urban scaling, finds that AIDS cases in the United States in 2002-2003 scale with the 1.23 power of city size. This result does not address the question about correlation and causation, nor does it clarify the temporal vs. cross-sectional issue. Later, Patterson-Lomba et al. (2015) conducted a broader analysis of the relationship between STDs and city size and found that STDs scale at a superlinear rate; that is, a person living in a big city is more likely to be infected with an STD than a person in a small city. They look at annual counts of chlamydia, gonorrhoea and syphilis from 2007 to 2011 in the 48 contiguous US states. The scaling exponents for these diseases are, respectively, 1.04, 1.10, and 1.29, and superlinear scaling remains robust to controls for socioeconomic status. Rocha, Thorson, and Lambiotte (2015) find superlinear growth in cases of HIV in Brazil and the US and also of chlamydia in the US.
CCS can also break down with environmental reservoirs, such as with cholera. Penrose et al. (2010) is one of several studies that finds a positive association with cholera risk and population density and informal settlements, though they argue that the true causal mechanism is poor sanitation infrastructure, for which density and informality are proxies. Furthermore, as is well-known, Azman et al. (2018) point out that cholera has been virtually eliminated in all large, wealthy cities through sanitation.
Influeza
Influenza is also not described well by the CCS model because of its global source and sink pattern. Here, the relationship between city size and flu prevalence is complicated.
Dalziel et al. (2018) examine the shape of annual flu outbreaks across cities. There is an obvious climate signal, with flu outbreaks more severe in colder climates. Correcting for that, they find that in smaller cities, outbreaks tend to be shorter and more severe, while in larger cities, outbreaks tend to be longer and less severe. These patterns stem from the fact that transmission rates are higher in larger cities due to greater amounts of personal contact. This is a good illustration of how, with a disease that confers immunity on a person, there is not necessarily a straight relationship from higher transmission rates to more severity. Larger cities have the advantage of beginning their transmission earlier, before the most favorable climactic conditions for the flu take hold, by which time a larger share of the population has developed immunity.
Rocha, Thorson, and Lambiotte (2015) consider a scaling relationship between the 2009-2010 swine flu pandemic in Brazil and city size. They find a scaling exponent of 1.20 in 2009 and 1.00 in 2010, indicating a change from one year to the next in cities’ public health responses.
The Spanish Flu (1918-1920) was one of the worst pandemics in world history, even deadlier than COVID-19 and at a time when the world population was less than a quarter of its present value. Acuna-Soto, Viboud, and Chowell (2011) find that deaths in the U.S. varied sublinearly with city population size with a scaling exponent of 0.81. It is not clear why this is the case, though the authors suggest that lower socioeconomic status in smaller cities might be the explanation. Clay, Lewis, and Severnini (2015) find that the degree of air pollution is a major factor in explaining excess deaths from the Spanish Flu, with public health, poverty, and the timing of the onset of the disease important factors as well.
COVID-19
As might be imagined, there is a large volume of literature related to city size and density and COVID-19 outcomes. One of the early studies is “Hamidi, Sabouri, and Ewing (2020)”, which finds that population density is not related to the numbers of COVID-19 cases and deaths, but city connectivity is. This was determined by regressing on data in 913 U.S. counties. “Carozzi, Provenzano, and Roth (2022)” find that initially, COVID-19 deaths were higher in denser countries, but by the end of 2020, this had turned into a flat relationship. Evidently denser counties were hit earlier but not harder.
References
Bartlett, M. S. “Measles Periodicity and Community Size”. Journal of the Royal Statistical Society: Series A (General) 120(1), pp. 48-60. 1957.
Bartlett, M. S. “The Critical Community Size for Measles in the United States”. Journal of the Royal Statistical Society. Series A (General) 123(1), pp. 37-44. January 1960.
Black, F. L. “Measles endemicity in insular populations: Critical community size and its evolutionary implication”. Journal of Theoretical Biology 11(2), pp. 207-211. July 1966.
Furuse, Y., Suzuki, A., Oshitani, H. “Origin of measles virus: divergence from rinderpest virus between the 11th and 12th centuries”. Virology Journal 7(1): 52. March 2010.
Keeling, M. J., Grenfell, B. T. “Disease Extinction and Community Size: Modeling the Persistence of Measles”. Science 275(5296), pp. 65-67. January 1997.
Grunning, C. E., Wearing, H. J. “Probabilistic measures of persistence and extinction in measles (meta)populations”. Ecology Letters 16(8), pp. 985-994. August 2013.
Conlan, A. J. K., Grenfell, B. T. “Seasonality and the persistence and invasion of measles”. Proceedings of the Royal Society B: Biological Sciences 274(1614): 1133. February 2007.
Bjørnstad, O.N., Finkenstädt, B.F., Grenfell, B.T. “Dynamics of measles epidemics: estimating scaling of transmission rates using a time series SIR model”. Ecological Monographs 72(2), pp. 169-184. May 2002.
Metcalf, C.J., Hampson, K., Tatem, A.J., Grenfell, B.T., Bjørnstad, O.N. “Persistence in epidemic metapopulations: quantifying the rescue effects for measles, mumps, rubella and whooping cough”. PloS one 8(9): e74696. September 2013.
McQuillan, G., Kruszon-Moran, D., Flagg, E.W., Paulose-Ram, R. “Prevalence of herpes simplex virus type 1 and type 2 in persons aged 14–49: United States, 2015–2016”.
Bettencourt, L.M., Lobo, J., Helbing, D., Kühnert, C., West, G.B. “Growth, innovation, scaling, and the pace of life in cities”. Proceedings of the National Academy of Sciences 104(7), pp. 7301-7306. April 2007.
Patterson-Lomba, O., Goldstein, E., Gómez-Liévano, A., Castillo-Chavez, C., Towers, S. “Per capita incidence of sexually transmitted infections increases systematically with urban population size: a cross-sectional study”. Sexually Transmitted Infections 91(8), pp. 610-614. December 2015.
Rocha, L.E., Thorson, A.E., Lambiotte, R. “The Non-Linear Health Consequences of Living in Larger Cities”. Journal of Urban Health 92(5), pp. 785-799. October 2015.
Penrose, K., Castro, M.C., Werema, J., Ryan, E.T. “Informal Urban Settlements and Cholera Risk in Dar es Salaam, Tanzania”. PLoS Neglected Tropical Diseases. 2010 Mar 16;4(3):e631.
Azman, A.S., Luquero, F.J., Salje, H., Mbaïbardoum, N.N., Adalbert, N., Ali, M., Bertuzzo, E., Finger, F., Toure, B., Massing, L.A., Ramazani, R. “Micro-Hotspots of Risk in Urban Cholera Epidemics”. The Journal of Infectious Diseases 218(7), pp. 1164-1168. August 2018.
Dalziel, B.D., Kissler, S., Gog, J.R., Viboud, C., Bjørnstad, O.N., Metcalf, C.J., Grenfell, B.T. “Urbanization and humidity shape the intensity of influenza epidemics in U.S. cities”. Science. 2018 Oct 5;362(6410):75-9.
Acuna-Soto, R., Viboud, C., Chowell, G. “Influenza and Pneumonia Mortality in 66 Large Cities in the United States in Years Surrounding the 1918 Pandemic”. PLoS One 6(8): e23467. August 2011.
Clay, K., Lewis, J., Severnini, E. “Pollution, Infectious Disease, and Mortality: Evidence from the 1918 Spanish Influenza Pandemic”. The Journal of Economic History 78(4), pp. 1179-1209. December 2018.
Hamidi, S., Sabouri, S., Ewing, R. “Does Density Aggravate the COVID-19 Pandemic? Early Findings and Lessons for Planners”. Journal of the American Planning Association 86(4), pp. 495-509. October 2020.
Carozzi, F., Provenzano, S., Roth, S. “Urban density and COVID-19: understanding the US experience”: The Annals of Regional Science 72(1), pp. 163-194. January 2024.