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The pace of life in the city: urban population size dependence of the dynamics of disease, crime, wealth and innovation Luís M. A. Bettencourt Theoretical Division Los Alamos National Laboratory ASU - February 4, 2006 Collaboration & Support:

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The pace of life in the city:urban population size dependence of the dynamics of disease, crime, wealth and innovation

Luís M. A. Bettencourt

Theoretical Division

Los Alamos National Laboratory

ASU - February 4, 2006


Collaboration & Support:

José Lobo : Global Institute of Sustainability, ASU

Geoffrey West: Santa Fe Institute

Dirk Helbing & Christian Kuhnert, T.U. Dresden

Support from ISCOM: European Network of Excellence

Special thanks to Sander van der Leeuw:

School of Human Evolution and Social Change, ASU


Scaling in Biological Organization

R=R0 Mb b=3/4 Power law solves: R(a N)=ab R(N)

Scale Invariance


  • Cells in organisms are constrained by resource distribution networks:

  • Hierarchical Branching

  • [3d] Space filling

  • Energy Efficient

  • Terminate at invariant area units

Total metabolic rate metabolic rate/mass

Larger organisms are slower!!


The city as a ‘natural organism’

Until philosophers rule as kings or those who are now called kings

and leading men genuinely and adequately philosophize, that is,

until political power and philosophy entirely coincide, […]

cities will have no rest from evils,...

nor, I think, will the human race.

Plato: [Republic 473c-d]

Raphael's School of Athens (1509-1511)

[…] it is evident that the state [polis] is a creation of nature,

and that man is by nature a political animal.

The proof that the state is a creation of nature and prior to

the individual is that the individual, when isolated, is not

self-sufficing; and therefore he is like a part in relation to the whole.

Aristotle: Politics [Book I]


Is there are analogue betweenbiological and social scaling?

  • Metabolic Rates ~ Nd/(d+1)

  • Energy/resource consumption

  • Rates decrease ~N-1/(d+1)

  • Times increase ~N1/(d+1)

  • Is 3> d ~2 ?

  • We set forth to search for data and estimate power laws:

  • Y(N)=Y0 Nb


Energy consumption vs. city size

Germany: year 2002

Data source:

German Electricity

Association [VDEW]

Courtesy of

Christian Kuehnert

super-linear

growth

economy

of scale


Structural Infrastructureoptimized global design for economies of scale

Note that although there are economies of scale in cables the network is still delivering energy at a superlinear rate:

Social rates drive energy consumption rates, not the opposite


Basic Individual needsproportionality to population

Also true for the scaling of number of housing units


The urban economic miracleacross time, space, level of development or economic system


Innovation as the engine

* France/1999 data courtesy Denise Pumain, Fabien Paulus


Innovation measured by Patents

Source data:

U.S. patent office

Includes all patents between 1980-2001

From “Innovation in the city: Increasing returns to scale in urban patenting”

Bettencourt, Lobo and StrumskyData courtesy of Lee Fleming, Deborah Strumsky


Employment patterns

b=1.15 ( 95% C.I.=[1.11,1.18] )

adjusted R2= 0.89

Data courtesy of Richard Florida and Kevin Stolarick.

Plot by Jose Lobo

Supercreative professionals [Florida 2002, pag. 327-329] are “Computer and Mathematical, Architecture and Engineering, Life Physical and Social Sciences Occupations, Education training and Library, Arts, Design, Entertainment, Sports and Media Occupations”.

Derived from Standard Occupation Classification System of the U.S. Bureau of Labor Statistics


Social Side Effects

Disease transmission is a social contact process:

Standard Incidence


The Pace of Life walking speed vs. population

Borstein & Bornstein

Nature 1976

Bornstein, IJP 1979

b

CI [0.071,0.115]


But cities to exist at all must also satisfy:

Basic individual needs (house, job, basic necessities)

Require city-wide infrastructure:

- larger population Optimization of system level

- higher density distribution networks

Result: 3 categories:

Social - interpersonal interactions - grow with # effective relations

Individual - no interactions - proportional to population

Structural - global urban optimization - economies of scale

Scaling Law:


Scale, Pace and Growth

Consider the energy balance equation:

growth

costs

available

resources

General Solution:


b<1 implies limited carrying capacitybiological population dynamics


b>1 : Finite time Boom and Collapse


Escaping the singularity with b>1:cycles of successive growth & innovation

tcrit shortens with N


Consequences for epidemiology

Epidemic dynamics

over quasi-static background

Consider:

Disease free fixed point:

Endemic fixed point:

m is a small parameter


b>1

1

b<1

N

dynamics at disease free fixed point

Unstable if:

b=1

Even if initially stable b>1 eventually

leads to endemic state.


b=1

b<1

N

Dynamics at endemic steady state

Infected as a fraction of the population:

b>1


Oscillations and decayat endemic state

Eigenvalues:

Solution:

w(N)

h(N)

b>1

b>1

b=1

b=1

b<1

b<1

N

N


General picture

Human social organization is a compromise over many social activities

Epidemiological dynamics is affected by large-scale

human organization and behavior


An argument for the smallness of the superlinearity in social scaling exponents

It is expected that a social process scales with the number of contacts.

Naively for a homogeneous population N:

Or per capita ncpc=(N-1)/2

Clearly in a large population, N>1000, not all contacts can be realized.

This naïve estimate is the wrong result, an unattainable upper bound.


Now, still assume that the number of effective contacts increases with N but is constrained (time, cognition, energy) to be much smaller:

between largest

and smallest city

Now equate the change in productivity per capita R= R1Nb-1 with this increase in effective contacts:

Note that ncpc(N) may itself scale, but with a very small exponent


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