We examine conditions under which high prevalence of infectious disease can become endemic within a community, in effect constituting a state of &#x27;herd infection&#x27; inverse to epidemiological herd immunity. For something like AIDS, under such circumstances, a single behavioral lapse or adverse accident will probably be a death sentence

Rodrick Wallace

English

Nature Precedings

Herd Immunity/Herd Infection:
Cultural Artifacts of Marginalization
and the Dynamics of AIDS
Rodrick Wallace, PhD
Division of Epidemiology
The New York State Psychiatric Institute∗
March 31, 2011
Abstract
We examine social conditions under which high prevalence of infectious
disease can become endemic within a community, in effect constituting
a state of ‘herd infection’ inverse to epidemiological herd immunity. For
something like AIDS, under such a circumstance, a single behavioral lapse
or adverse accident will probably be a death sentence.
1 Introduction
The form of a social network and the behaviors of those within it are cultural
artifacts reflecting both current conditions and historical trajectory: Culture is
both dynamically and historically configured, and represents a third system of
human heritage beyond the genetic and biochemical epigenetic (e.g., Boyd and
Richerson, 2004; Richerson and Boyd, 2005; Jablonka and Lamb, 1995). Here
we will examine the role of marginalization and oppression in creating a kind
of superhighway for pandemic infection within affected communities, and use a
formal model to explore the insight of L. Beane (2011) that a kind of mirror
image to epidemiological herd immunity might be possible, i.e., a ‘herd infection’
sufficient to virtually guarantee the infection of susceptible individuals within a
population.
The argument we pursue has two sections. The first focuses on conditions
under which a ‘giant component’ emerges within a networked population of
sucseptibles allowing the propagation of infection to a significant fraction of it.
The second involves the production of ‘risk behaviors’ for infection within that
population. It will be seen that social network structure and the generation of a
‘behavioral vocabulary’ that may accelerate infection transmission are not only
∗Box 47, 1051 Riverside Drive, NY, NY, 10032. rodrick.wallace@gmail.com
1
N
at
ur
e 
Pr
ec
ed
in
gs
 : 
hd
l:1
01
01
/n
pr
e.
20
11
.5
86
4.
1 
: P
os
te
d 
31
 M
ar
 2
01
1
intertwined but synergistic, and strongly determined by current and historical
power relations between groups.
This is, overall, quite straightforward, and leads directly to Beane’s concept
of herd infection.
2 Epidemic threshold and social network struc-
ture
The basic idea of herd immunity is that there is a threshold of vaccination for
a population above which an infectious disease cannot propagate. Typically,
for diseases like measles, chickenpox, and diphtheria, 85-95% vaccination rates
prove sufficient to prevent chains of infection within a general population, thus
protecting unvaccinated individuals (on the whole) from the diseases. A classic
model based on differential rate equations can be found in many places (e.g.,
Bailey, 1975). The underlying assumption of the model is that probability of
contact between individuals is random. Nonrandom contact patterns do not
necessarily show similar dynamics, for example if nonvaccinated individuals are
all closely connected, e.g., members of a particular political, religious, or other
subgroups that interact regularly. This insight can be made in a formal manner
by considering social network topology.
Some fifty years ago Erdos and Renyi (1960) explored the emergence of a
highly interconnected ‘giant component’ in random networks. Following the
review by Spenser (2010) closely (see, e.g., Boccaletti et al., 2006, for more
detail), assume there are n network nodes and e edges connecting the nodes,
distributed in a uniform probability distribution – no clustering. Let G[n, e] be
the state when there are e edges. The central question is the typical behavior of
G[n, e] as e changes from 0 to (n−2)!/2. The latter expression is the number of
possible pair contacts in a population having n individuals. Another way to say
this is to let G(n, p) be the probability space over graphs on n vertices where
each pair is adjacent with independent probability p. The behaviors of G[n, e]
and G(n, p) where e = p(n− 2)!/2 are asymptotically the same.
Parameterize as p = c/n. The graph with n/2 edges then corresponds to
c = 1. The essential finding is that the behavior of the network has three
sections. If c < 1 all the linked subnetworks are very small. If c = 1 there is
a single large interlinked component of a size ≈ n2/3. If c > 1 then there is a
single large component of size yn where y is the positive solution to the equation
exp(−cy) = 1− y.
Then
y =
W (−c/ exp(c)) + c
c
,
where W is the Lambert W function.
2
N
at
ur
e 
Pr
ec
ed
in
gs
 : 
hd
l:1
01
01
/n
pr
e.
20
11
.5
86
4.
1 
: P
os
te
d 
31
 M
ar
 2
01
1
The solid line in figure 1 shows y as a function of c, representing the fraction
of network nodes that are incorporated into the interlinked giant component.
To the left of c = 1 there is no giant component, and large scale transmission of
infection is not possible. The role of vaccination in a random population is to
drive c below that limit.
The dotted line, however, represents the fraction of nodes in the giant com-
ponent for a highly nonrandom social network, a star-of-stars-of-stars (SoS) in
which every node is directly or indirectly connected with every other one. In
such a case there is no threshold, only a single giant component: Introduction
of infection to any node of the network produces infection across the entire
network.
The essential argument is that, for the SoS network and analogous topolo-
gies, once disease has been introduced into the community, any individual ‘risk
behavior’ interaction with the network guarantees infection, the precise inverse
of herd immunity, as Beane has speculated.
Are there any SoS-like networks in the real world? Carol Stack’s (1974) book
All Our Kin: Strategies for Survival in a Black Community describes underlying
mechanisms of resource sharing and obligation that necessarily include patterns
of intimate contact between sexes. A more recent paper by Murrill et al. (2008)
examines a similar network within gay and transgender African-Americans that
had been described in the documentary film Paris is Burning. The House
Ball community “...is rooted in Black traditions of communal social support
in response to economic and social exclusion. It functions as a kinship system
that is organized to meet the needs of its members for social solidarity and
mentoring...”. Of the 504 study participants, nearly one-fifth were HIV-positive,
some three-quarters of these individuals unaware of their infection status.
3 Marginalization and behavioral coding
Wallace et al. (1996) explore a mathematical model in which ‘risk behaviors’
for infection constitute essential components of a behavioral code for the trans-
mission of information within the noisy channel of a marginalized community’s
social networks. The code’s form, including the incorporation of risk behaviors,
arises as a direct consequence of the external oppressive forces which structure
marginalization. This perspective contributes to an explanation for the rapid
transmission of infection along a social network. Further, in the face of ‘be-
havioral’ interventions, if risk behaviors are parts of a behavioral code for the
transmission of group norms, statements of individual worth or resource sharing,
then high rates of relapse are inevitable, given the persistence of the external
oppression that gives those behaviors symbolic value. Wallace et al. found that
violent acts in particular may emerge as key behavioral symbols for sending
a message in socially disorganized communities, creating further social disor-
ganization in a destabilizing positive feedback. They call for comprehensive,
multifactorial reform to reverse the effects of continuing economic and social
constraints or public policies of ‘planned shrinkage’ and ‘benign neglect’ and
3
N
at
ur
e 
Pr
ec
ed
in
gs
 : 
hd
l:1
01
01
/n
pr
e.
20
11
.5
86
4.
1 
: P
os
te
d 
31
 M
ar
 2
01
1
Figure 1: Fraction of network nodes in the giant component as a function of the
coupling parameter c. The solid line represents a random graph, the dotted line
a star-of-stars-of-stars network in which all nodes are interconnected. Only for
the random network, when c < 1, is ‘herd immunity’ possible.
4
N
at
ur
e 
Pr
ec
ed
in
gs
 : 
hd
l:1
01
01
/n
pr
e.
20
11
.5
86
4.
1 
: P
os
te
d 
31
 M
ar
 2
01
1
serial forced migration responsible for the disorganization of urban minority
communities in the US.
Such a ‘behavioral code’ perspective is consonant with any number of an-
thropological studies. Aggleton et. al. (1994), for example, write
Although sex has a biological function, it is one of the most
socially diverse of human activities, and although sexual behavior
has a certain biological similarity across the globe, the meaning of
sex differs profoundly between cultures and even within societies.
This means that the role and purpose of the ‘same’ biological act
may be seen quite differently from culture to culture...
A number of factors other than risk perception influence the
extent to which an individual will consistently take steps to pro-
tect against infection... in many contexts, the scope for individual
decision-making is limited by the greatly under-recognized fact that
behavioral change is not solely dependent on individual volition.
The relevance of social factors that contribute to risk behavior and
the importance of modifying these social factors to enable HIV risk
reduction are greater than in almost all other fields of health and
behavior...
4 Discussion and conclusions
Marginalization and oppression – the essence of the power relations between
groups in Western culture – act synergistically to produce both social network
topologies and behavioral codes that constitute risks for the transmission of
pandemic infection under a broad spectrum of circumstances. For AIDS in
particular, that synergism seems capable of producing a condition of ‘herd in-
fection’ within African-American and Gay male subgroups that often makes a
single behavioral lapse a death sentence. The ‘pharamceuticalization’ of AIDS
in the US – the view that drug treatment of infected individuals constitutes a
population-level control strategy – guarantees the evolution of multiply-drug-
resistant varieties of HIV in oppressed communities, given the nature of the virus
as a relentless evolution machine (Wallace et al., 2009, Section 6.3). MDR-HIV
will inevitably diffuse outward from these centers of chronic infection to become
a scourge even for those who create, endorse, or tolerate the social conditions
producing the fatal synergism we have examined: One possible evolutionary
route for HIV is a deadly change in life history strategy that will not see infec-
tion confined to marginalized populations in Western societies (R.G. Wallace,
2004).
5 References
Aggleton, P., K. O’Reilly, G. Slutkin, P. Daves, 1994, Risking everything? risk
behavior, behavior change and AIDS, Science, 265:341-347.
5
N
at
ur
e 
Pr
ec
ed
in
gs
 : 
hd
l:1
01
01
/n
pr
e.
20
11
.5
86
4.
1 
: P
os
te
d 
31
 M
ar
 2
01
1
Beane, L., 2011, personal communication.
Bailey, N., 1975, The Mathematical Theory of Infectious Diseases and its
Applications, Hafner, New York.
Boccaletti, S., V. Latora, Y. Moreno, M. Chavez, D. Hwang, 2006, Complex
networks: structure and dynamics, Physics Reports, 424:175-308.
Boyd, R., P. Richerson, 2004, The Origin and Evolution of Cultures, Oxford
University Press.
Erdos, P., A. Renyi, 1960, On the evolution of random graphs, Magyar Tud.
Akad. Mat. Kutato Int. Kozl, 5:17-61.
Jablonka, E., M. Lamb, 1995, Epigenetic Inheritance and Evolution: The
Lamarckian Dimension, Oxford University Press, Oxford, UK.
Murrill, C., K. Liu, V. Guillin, E. Rivera Colon, L. Dean, L. Buckley, T.
Sanchez, T. Finlayson, L. Torian, 2008, HIV prevalence and associated risk
behaviors in New York City’s house ball community, American Journal of Public
Health, 98:1074-1080.
Richerson, P., R. Boyd, 2005, Not by Genes Alone: How culture transformed
human evolution, University of Chicago Press.
Spenser, J., 2010, The giant component: the golden anniversary, Notices of
the AMS, 57:720-724.
Stack, C., 1974, All Our Kin: Strategies for Survival in a Black Community,
Basic Books, New York.
Wallace, R., M. Fullilove, A. Flisher, 1996, AIDS, violence and behavioral
coding: information theory, risk behavior and dynamic process on core-group
sociogeographic networks, Social Sicence and Medicine, 43:339-352.
Wallace, R., D. Wallace, R.G. Wallace, 2009, Farming Human Pathogens:
Ecological Resilience and Evolutionary Process, Springer, New York.
Wallace, R.G., 2004, Projecting the impact of HAART on the evolution of
HIV’s life history, Ecological Modelling, 176:227-253.
6
N
at
ur
e 
Pr
ec
ed
in
gs
 : 
hd
l:1
01
01
/n
pr
e.
20
11
.5
86
4.
1 
: P
os
te
d 
31
 M
ar
 2
01
1


AIDS, violence and behavioral coding: information theory, risk behavior and dynamic process on core-group sociogeographic networks, Social Sicence and Medicine,

All Our Kin: Strategies for Survival in a Black Community, Basic Books,

Epigenetic Inheritance and Evolution: The Lamarckian Dimension,

Farming Human Pathogens: Ecological Resilience and Evolutionary Process,

HIV prevalence and associated risk behaviors in New York City's house ball community,

Not by Genes Alone: How culture transformed human evolution,

On the evolution of random graphs,

Projecting the impact of HAART on the evolution of HIV's life history, Ecological Modelling, 176:227-253. N a t u r e P r e c e d i n g s : h d l : / n p r e

Risking everything? risk behavior, behavior change and AIDS, Science, 265:341-347. N a t u r e P r e c e d i n g s : h d l : / n p r e

The giant component: the golden anniversary,

The Mathematical Theory of Infectious Diseases and its Applications,

The Origin and Evolution of Cultures,

Herd Immunity/Herd Infection: Cultural Artifacts of Marginalization and the Dynamics of AIDS

http://precedings.nature.com/documents/5864/version/1

Herd Immunity/Herd Infection: Cultural Artifacts of Marginalization and the Dynamics of AIDS

Abstract

Similar works

Full text

Available Versions

Nature Precedings