Good healthcare and leaky ostracism make stigmas against infectious
disease maladaptive
2
4
Timothy C. Reluga1,* , Rachel A. Smith2 , David P. Hughes3 ,
1 Department of Mathematics, Center for Infectious Disease Dynamics, The
Pennsylvania State University, University Park, PA 16802
2 Department of Communication Arts and Sciences, Center for Infectious Disease
Dynamics, and The Methodology Center, Pennsylvania State University, University
Park, PA 16802
3 Departments of Entomology and Department of Biology, Center for Infectious
Disease Dynamics, Pennsylvania State University, University Park, PA 16802
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8
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* timothy@reluga.org
Abstract
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Stigmas are a primal phenomena, ubiquitous in human societies past and present. Some evolutionary anthropologists have argued that stigmatization in response to disease is an adaptive behavior,
that may help people and communities reduce the risks they face from infectious diseases and increase
reproductive success. At the same time, cultural anthropologists and social critics have argued that
stigmatization has strong negative impacts on community health. Recent analyses have resolved
this conflict by hypothesizing that stigmas had individual and group-evolutionary benefits early in
human evolution may now be mal-adaptive.
Here, we present the first quantitative theory of infectious disease stigmatization and its consequences. We propose a four-state model of the stigmatization process driven by a transmissible
disease creating chronic infections, and explore how rates of stigmatization can interact with social
structure to impact the prevalence and lifetime risks of infection. The affects of stigmatization are
revealed to be strongly dependent on health and cultural contexts. The asymmetries in secondary
transmission between stigmatized and unstigmatized individuals can be represented with a dimensionless statistic Z , which we call the “stigma ratio”. When stigmatized people are strongly segregated
from the rest of the population and there are no alternative interventions that reduce transmission
(Z > 1), stigmatization can reduce lifetime risk of infection and overall disease prevalence. But
when stigmatization is weakly enforce and reduces access to medical and behavioral interventions
(Z < 1), stigmas increase lifetime risk and may increase prevalence. We further show fear of stigmas
can exacerbated these negative effects and drive policy resistance against testing and treatment. We
conclude that the deprecation of stigmas is a natural transition in the modern urban societies.
Key words: Stigma; Ostracism; Infectious Disease Dynamics; Cultural Evolution Theory; Group
Membership; Math Modelling;
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1. Introduction
Disease has been one of the strongest evolutionary pressures on Homo sapiens over the duration
38
of our species’ existence, and indeed on all mammalian species. Bacteria, fungi, protozoa, worms, and
all manner of parasites have caused the untimely deaths of tens of billions of our potential ancestors,
40
driving us to evolve a complex immune system that learns about, adapts to, and remembers the
infections we suffer over our lives [1, 2]. This same evolutionary pressure has also been operating
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on human instinct for millennia, leading to innate behaviors like hygiene [3] and stigmatization [4].
However, while hygiene continues to be universally valued, stigmatization is now contentious.
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Stigmas are considered a leading [e.g. 5] and poorly understood [e.g. 6] barrier to disease
prevention, control, and treatment. Stigma has been linked to delayed diagnosis, poor treatment
46
adherence, prolonged risk of transmission, and increased risks of recurrence [e.g. 7] among other
things. Stigmas are defined as simplified, standardized images of the profound disgrace of a particular
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social group shared by a community at large [8]. But stigmas mark more than difference: they
designate someone as profoundly devalued, discredited, and disgraced [9]. Among humans, stigmas
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are socialized: community members need to be able to recognize those who pose threats to their
group and how to limit this stigmatized group’s access to group resources and future interactions.
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Consequently, humans developed messages to meet these goals. To stimulate stigma-related processes
(creating beliefs, and inspiring actions to isolate and remove the labeled, and to socialize others), these
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messages need to include content that quickly gains attention, encourages grouping and stereotyping,
and provides reasons and emotional motivation to engage in devaluation and discrimination [10].
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Although stigmas can be a significant barrier to health, they are ubiquitous in human societies,
globally and historically [8]. They even appear in other social species, from ants to chimpanzees
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[11, 12, 13]. Scholars have proposed several hypotheses to explain this ubiquity of stigmas despite
their costs. Some scholars [15] argue that stigmas defend group functioning. Some feel stigmas may
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be a side effect of the evolution of discriminate sociality [4]. Others [16, 17] believe that they evolved
as a defense against infectious diseases. Infectious diseases capitalize on the social nature of groups,
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by spreading from one person to another via their interactions [14]. For social species who depend on
each other for survival, stigmas may have functioned to protect uninfected members and the group,
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by identifying infected members and ostracizing them from the group.
For an infected person in a band or tribe millennia ago, ostracism meant swift and certain
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death due to the infection, lack of resources and vulnerability to predators [13, 14]. For most of
human history, particularly during the paleolithic period, humans lived in small, family-based groups,
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with infrequent, intergroup interactions (typically for mating). This evolutionary advantage, then,
occurred in pre-urban times (3000 years ago and older), when ostracized members would not be
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brought into other groups. Ostracism, then, stopped the spread of infection and eliminated a reservoir
for future infections.
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Over the past 3,000 years, many conditions for the human species have changed – the population
has grown, transportation facilitated widespread contact between humans, and medical practices
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provided treatments for infectious diseases, all of which have implications for slowly evolving behaviors
[18]. Smith and Hughes [14] explained how these new conditions could eliminate any fitness advantage
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provided by stigmas, and, in fact, damage public health. For example, ostracism from one group no
longer guarantees isolation from others. In addition, humans are noted for their sensitivity to social
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rejection, with initial reactions to it registering like physical pain [19]. The social cost may be so
high that people will keep suspected infections secret and avoid interacting with medical systems
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altogether, which eliminates their ability to access medical treatments for the infection [10].
However, to understand how stigmatization transitions from an advantageous to a disadvantageous
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behavior, we have to quantify the impacts of each of these changes in behavior. When do stigmatization’s benefits from infectious disease risk reduction stop offsetting the it’s social costs? In this paper,
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we propose a nonlinear 4-state compartmental theory for the interactions between stigmatization
and infectious disease prevalence. Our theory projects disease prevalence and community size under
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steady-state conditions using demographic parameters, infection risks, and behavior. We use this
model to determine conditions when stigmatization hurts public health. The theory can be extended
and applied in many contexts to estimate the public-health impact of stigmatization.
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2. Materials and Methods
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In this section, we will describe the mathematical model of our theory of the interactions between
stigmatization and disease-transmission dynamics. Our model combines a 4-state Markov chain for
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the changes in an individual’s disease state with a reaction-network of nonlinear ordinary differential
equations for disease prevalence. Definitions of our variables are provided in Table 1, while definitions
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of our parameters and estimates for model scenarios are shown in Table 2.
Table 1. State variables used in our model. Without brackets, the variable is a probability, but
with brackets, the variable is a density.
Symbol Meaning
t
Time measured in years
S(t)
Probability of being susceptible
C(t)
Probability of being cryptically infected
L(t)
Probability of being labelled with infection
Z(t)
Probability of begin stigmatized with infection
[S](t)
Density of susceptible people
[C](t)
Density of cryptically infected people
[L](t)
Density of people labelled with infection
[Z](t)
Density of people stigmatized with infection
Each person in our model is categorized in one of four possible states: susceptible, cryptically
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infected, infected and labelled, or infected and stigmatized. The probabilities that a person is in
each of these states is represented respectively by S(t), C(t), L(t), and Z(t), where t represents time,
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measured in years. A person can also leave the system because of death. Each individual is initially
susceptible, so S(0) = 1 while C(0) = L(0) = Z(0) = 0. Transitions between states are governed by a
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continuous-time Markov chain summarized in Figure 1. A susceptible person can become cryptically
infected (rate Λ), a cryptically infected person can become labelled (rate x), labelled person can be
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stigmatized (rate y). Death rates may depend on the person’s state (mS , mC , mL , mZ ). In matrix
form, the probabilities of being in each state change according to the matrix equation


−mS − Λ

 

 
dC/dt 
Λ

 

=

 
0
 dL/dt  

 
dZ/dt
0
dS/dt

0
0
−mC − x
0
x
−mL − y
0
y
4
 
S
 
 
 
0 
 C 
 .
 
0  L
 
−mZ
Z
104
0
(1)
Table 2. Parameters used in our model, their meanings, and the estimated values used in Old and
New Scenarios. To facilitate plot comparisons, we choose the transmission rate β so that in all
scenarios in the absence of stigmatization or labelling (y = x = 0), the basic reproductive ratio
R0 = 2. The stable population sizes in Scenarios 1 and 2 are respectively N = 100 and N = 10, 000.
Meaning
Immigration rate of susceptible people
Death rate while susceptible
Death rate while crypticly infected
Death rate while labelled
Death rate while stigmatized
Rate infected become labelled
Rate labelled become stigmatized
Background infection hazard
Transmission rate when crypticly infected
Relative transmission rate once labelled
Relative transmission rate once stigmatized
Marginal value per time of being in state S
Marginal value per time of being in state C
Marginal value per time of being in state L
Marginal value per time of being in state Z
Stigma ratio
Parameter
b
mS
mC
mL
mZ
x
y
β
σ
η
uS
uC
uL
uZ
Z
Scenario 0
(Non-infectious)
2
0.02
0.02
0.02
0.2
12.0
2 × 10−2
0
NA
NA
NA
NA
NA
NA
NA
Scenario 1
(Pre-Urban)
2
0.02
0.1
0.1
0.2
1.0
10−3
2 × 10−3
1.0
0.01
1
0.8
1.
0.
200
Scenario 2
(Modern)
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0.02
0.1
0.04
0.04
1.0
10−5
2 × 10−5
0.1
0.5
NA
NA
NA
NA
0.2
Our reaction network is an extension of classic compartmental models for epidemic dynamics
[33, 34, 35]. It describes the change in the population health over time t under the assumption that
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the population is strongly mixed, and all individuals have equal frequencies of contact with each other.
Two new states are added to the classical compartmental epidemic model of chronic infectious disease
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transmission to count when people have been labelled and stigmatized. We modify the notation
slightly from standard practice for readability. Let [S](t) be the density of susceptible people who
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without signs of infection. Let [C](t) be the density of infected people whose state has not yet been
publicly identified. Let [L](t) be the density of people who are infected and have had their infection
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publicly identified, and let [Z](t) be the density of infected people who have been stigmatized for
their state. To avoid complications associated with demographic transients, we assume a constant
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immigration rate of susceptible people (b). Over time, susceptible individuals may become infected
through exposure to people in any of the infected compartments. We approximate the infection
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pressure Λ, a.k.a. the “infection pressure”, as a linear function of the density of infected individuals.
Λ = β ([C] + [L]σ + [Z]η) + ,
(2)
where can be interpreted as the background risk of infection from an environmental reservoir, β is
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the baseline transmission rate for cryptically infected people, and σ and η are relative transmission
rates compared to the cryptically infected for labelled and stigmatized categories respectively. This
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linear approximation is equivalent to the mass-action hypothesis in a strongly-mixed community
with an environmental disease reservoir, but is also good approximation near equilibrium other
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hypothetical forms of the infection pressure. Infected people become labelled at a constant rate,
labelled people become stigmatized at a constant rate. This leads to a system of 4 ordinary differential
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equations with one additional algebraic constraint:
d[S]
dt
d[C]
dt
d[L]
dt
d[Z]
dt
= b − [S]mS − [S]Λ,
(3a)
= [S]Λ − [C]mC − [C]x,
(3b)
= [C]x − [L]mL − [L]y,
(3c)
= [L]y − [Z]mZ ,
(3d)
Λ = β ([C] + [L]σ + [Z]η) + .
(3e)
Note that contact-reduction through stigmatization is a refinement of social distancing [36]. While
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social-distancing is applied equally to all contacts, stigmatizing selectively reduces contacts with
specific subpopulations.
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The basic reproductive ratio, which determines the persistence of disease when background
infection risks from reservoirs are very small ( ≈ 0) is
R0 =
bβ
mS
1
σx
ηxy
+
+
mC + x (mC + x) (mL + y) mZ (mC + x) (mL + y)
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.
(4)
When there is no stigmatization (y = 0),
R0 =
bβ (mL + σx)
.
mS mL (mC + x)
(5)
The steady-state lifetime risk ([LR], the probability of a person becoming sick over their lifetime) is
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Λ/(Λ + mS ).
We determine steady-state community sizes and disease prevalence by setting time-derivatives in
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System (3) to zero and deriving a quadratic equation for Λ.
Λ=
ΛmS R0
+ .
Λ + mS
(6)
As long as there is some environmental reservoir seeding infection ( > 0), there is a single steady-state
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infection pressure Λ∗ ∈ (0, βb/mS + ) which we calculate numerically and is monotone increasing
with both the basic reproductive ratio (R0 ) and the reservoir pressure (). The steady-state densities
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[S]∗ , [C]∗ , [L]∗ , and [Z]∗ can then all be calculated using linear algebra. The gross steady-state
population density is [S]∗ + [C]∗ + [L]∗ + [Z]∗ , while the prevalence is P ∗ := [C]∗ + [L]∗ + [Z]∗ .
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The effect of stigmatization on risk, infection pressure, and prevalence can be assessed through
differentiation. The infection pressure depends on stigmatization only through the basic reproductive
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ratio, according to Eq. (6). Differentiating the reproductive ratio, we find
bβx (ηmL − mZ σ)
dR0
=
2
dy
mS mZ (mC + x) (mL + y)
(7)
The impact of stigmatization can be summarized by defining a dimensionless stigma ratio
Z :=
σβ
mL
mZ
ηβ
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(8)
which represents the ratio of the average cumulative transmission of a labelled but unstigmatized
individual, and the average cumulative transmission of a stigmatized individual. Setting the derivative
of the reproductive ratio with respect to the stigmatization rate to zero, we find that if Z = 1,
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then basic reproductive ratio is independent of the rate of stigmatization. If Z < 1, then more
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stigmatization increases the reproductive ratio, but if Z > 1, then more stigmatization decreases the
reproductive ratio. Thus, the relationship between the stigmatization rate and the basic reproductive
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ratio is monotone, with a sign determined by the stigma ratio. Since the infection pressure is
a monotone function of the basic reproductive ratio, the same holds for it – if Z < 1, faster
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stigmatization increases the infection risk, but if Z > 1, faster stigmatization decreases the infection
risk.
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The stigma ratio Z depends on the mortality rates mL and mZ which can be altered by medical
treatment and state-correlated stresses. The value of the stigma ratio also depends on the relative
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transmission rates σ (for the labelled) and η (for the stigmatized), which incorporate changes in
contact rates and changes the probability of infection per contact. Changes in contact rate and
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infectiousness can be attributed to differences in medical treatment and behavior because of social
state. For example, the stigmatized might try to escape social stresses by avoiding medical treatment
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and beneficial behaviors that reveal their disease state, leading to a relative increase in η over σ, so
the stigma ratio Z will be small. On the other hand, if the stigmatized are ostracized (reducing η)
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and have lower survivorship (increasing mZ ), then the stigma ratio will be large. Parameters are
only summary statistics; the responses to stigmatization will be heterogeneous, with some people
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conforming to social norms while others rebel against the same norms, so in practice we have to
average over the effected population to estimate the stigma ratio.
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The stigma ratio does not itself tell the whole story. The effect of stigmatization on prevalence is
mathematically more complicated. The steady-state disease prevalence P ∗ has the matrix formula
 T
0
 
 
1
 
P∗ =  
 
1
 
1

−mS − Λ



Λ



0


0
0
0
−mC − x
0
x
−mL − y
0
y
8
−1  
b
  
  
 
0 
 0
  
  
0  0
  
−mZ
0
0
(9)
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Differentiating prevalence with respect to the stigmatization rate,
where
dP ∗
∂P ∗
∂P ∗ ∂Λ dR0
=
+
dy
∂y
∂Λ ∂R0 dy
∂P ∗
Λbx (mL − mZ )
=
2,
∂y
mZ (Λ + mS ) (mC + x) (mL + y)
∂P ∗
bmS (mL mZ + mZ x + mZ y + xy)
=
,
2
∂Λ
mZ (Λ + mS ) (mC + x) (mL + y)
∂Λ
Λ2 mS
ΛmS (Λ + mS )
= 2
=
2
2
∂R0
(Λ + mS ) − R0 mS
Λ + mS
and dR0 /dy is given in Eq. (7). From inspection, we can tell that ∂P ∗ /∂Λ > 0 and ∂Λ/∂R0 ≥ 0
Since stigmatization is never expected to improve life-expectancy (µL ≤ µZ ), ∂P ∗ /∂y ≤ 0. It then
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follows that whenever the stigma ratio Z > 1, faster stigmatization will reduce prevalence. There
doesn’t appear to be such a simple general condition for when stigmatization increases prevalence,
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but we can find some special cases. If stigmatization has no effect on mortality (µL = µZ ), for
instance, then Z < 1 implies faster stigmatization increases prevalence.
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The rate with which cryptically infected individuals are willing to seek out medical help and
be “out” about their condition can depend on the rate of stigmatization and it’s consequences. In
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communities where stigmatization is rapid and harsh, low rates of diagnosis and labelling (x small)
may prevent people from taking advantage of effective treatments and educational programs even
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when available. The rate at which people allow themselves to become labelled can be thought of
as an optimization problem. Using Markov decision-process theory [24, 25], we can show that the
expected utility of labelling at rate x in a population that stigmatizes at rate y is
U(x, y) :=
1
Λ + h + mS
uS +
Λ
h + mC + x
uC +
x
h + mL + y
uL +
yuZ
h + mZ
(10)
where ui represents the marginal value per time of residing in state i and h is the discount rate. This
expected utility is a hyperbolic function of the labelling rate x, so the best labelling rate will be
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either the largest or smallest value possible. Explicitly, by differentiation we find
xbest (y) := xmin +


(xmax − xmin )H 




uC   uL
uC 
y
 uZ
−
−

+

mL + h mZ + h mC + h
mL + h mC + h
(11)
where H() represents Heaviside’s step function. Commonly, the stigma state is less valuable than
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the labelled state (uZ /mZ < uL /mL when h = 0). If it is also worse to be cryptically infected
than labelled or stigmatized, (uC /mC < uZ /mZ ), then it’s best to maximize the labelling rate
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(xbest (y) = xmax ). If cryptic infection is better than stigma and labelling (uL /mL < uC /mC ), then
it’s best to minimize the labelling rate (xbest (y) = xmin ). If cryptic infection’s value falls between
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the values of stigma and labelling, the best behavior depends on the risk of stigmatization, and slow
labelling is optimal only if the stigmatization rate is large enough.
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When people acting in their own self-interest counter-act a community policy, we call it “policy
resistance”. When people’s actions reinforce and amplify a policy, we call it “policy reinforcement”.
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In this case, the policy is a cultural norm, that is beneficial at the community scale, If the stigma
ratio Z > 1 but the cryptic state is better for individuals than both labelled and stigmatized states,
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we expect to observe policy resistance. On the other hand, if the stigma ratio Z < 1 and the cryptic
state is worse than the labelled and stigmatized states, we expect to observe policy reinforcement.
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Epidemic theories that account for population heterogeneity are more complicated than the
homogeneous theory we have presented here, as they account for differences in health, age, and
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contact rate [37, 38, 39]. For a baseline model of stigmatization in a heterogeneous population, we
suggest a model where all individuals face the same risk, but may differ in all other parameters.
Specifically, individuals are distributed over a type-space Ω according to a measure µ(ω; y) which
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varies according to the stigmatization rate y. Then dynamically,
d[Sω ]
dt
d[Cω ]
dt
d[Lω ]
dt
d[Zω ]
dt
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= b − [Sω ]mS − [Sω ]Λ,
(12a)
= [Sω ]Λ − [Cω ]mC − [Cω ]x,
(12b)
= [Cω ]x − [Lω ]mL − [Lω ]y,
(12c)
= [Lω ]y − [Zω ]mZ ,
Z
Λ=
β ([Cω ] + [Lω ]σ + [Zω ]η) dµ(ω; y) + ,
(12d)
(12e)
ω∈Ω
where the parameter values (x, b, β, σ, η, uS , uC , uL , uZ ) are independent implicit functions of the
type ω ∈ Ω. The steady-state infection pressure is the unique solution of the quadratic equation
where
ΛmS R0 (y)
Λ=
+
Λ + mS
Z bβ
σx
ηxy
R0 (y) =
1+
+
dµ(ω; y)
mS (mC + x)
(mL + y) mZ (mL + y)
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(13a)
(13b)
ω∈Ω
with R0 (y) being the expected basic reproductive ratio for a heterogeneous population. For small
reservoir pressures ( → 0) and R0 > 1,
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Λ = mS (R0 (y) − 1) + R0 (y)
+ O(2 ).
R0 (y) − 1
(14)
From this approximation, the sensitivity of the lifetime risk to changes in the stigmatization rate
"
#
d [LR]
1 dR0
(2R(y) − 1)
2
= 2
1−
+O dy
R0 dy
mS (R(y) − 1)2
(15)
Thus, to minimize lifetime risk in a community without environmental reservoirs, it suffices to study
206
the effects of stigmatization on the basic reproductive ratio R0 . Our expression for the stigma ratio
Z can be derived from this in the special case of a homogeneous population.
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3. Modelling and Analysis
Infectious disease stigmas have several complications that make their quantitative theory challeng-
210
ing. Foremost, the concept of a stigma is fuzzily defined. Unlike infection, which is a biological state
that can be empirically tested using Koch’s postulates [20], a stigma is imposed on an individual
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by their neighbors and not a testable property of the individual. A statement that a person is
stigmatized is a communication about the perception of that person by the community, rather than
214
a statement about the person themselves. Moving a stigmatized person to a naive community may
relieve them from experiencing stigmatization, at least temporarily. In addition, lay assignment of
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infectious disease stigmas is imperfect. Humans rely on physical (often visual) and behavioral marks
to identify targets of stigmatization [21], even though hosts are often infected and able to spread
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disease to others before or even without showing symptoms [22]. Other conditions having generic
symptoms overlapping the specific disease can be mis-attributed. More insidiously, stigma criteria
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can drift because of people exploiting the situation for personal gain.
S
Λ
mS
C
x
L
y
mL
mC
Z
mZ
Figure 1. State-transitions for stigmatization. Here, S denotes the probability of being in
susceptible state, C is the probability of being in the cryptically infected state, L is the probability
of being in the labelled state, and Z is the probability of begin in the stigmatized state. See Tables 1
and 2 for parameter definitions and values.
While there are inherent challenges, the dynamic analysis of stigmas can still provide useful
222
insight. Our formal mathematical analysis is given in the Materials and Methods, and summarized
in Figure 1. People are categorized among four mutually-exclusive states: susceptible (S), cryptically
224
infected (C), infected and labelled (L), or infected and stigmatized (Z). Susceptible people are at risk
of infection when they interact with either other infected people or an environmental disease reservoir.
226
Infections are chronic and people remain infected for the rest of their lives, as in several current
and historical diseases that have generated stigmas. Infected people interact with susceptible people
in different ways, depending on whether the community is ignorant of their infection (cryptically
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228
infected), or has labelled or stigmatized them. Cryptically infected individuals interact with other
230
people normally, can transmit disease. But when the community becomes aware of the diagnosis
or identifies the symptoms or behavior change of a cryptically infected person, they transition to a
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labelled state – our math assumes that gossip of this sort permeates a community quickly. Once
people are labelled, they can still transmit infection but can also access doctors, hospitals, and
234
other medical resources publicly. However, the labelled are also at risk for stigmatization by their
community. Stigmas result in ostracism and reduced contacts with susceptibles. They may also
236
correspond to higher removal and mortality rates. Since there is no consistent and reliable means by
which to remove a stigma [14], stigmas persist indefinitely, although individuals may adopt a variety
238
of cooping mechanisms, with variable success and consequences. For simplicity and illustration, we
assume the infection pressure Λ obeys the generalized mass-action law Λ = β ([C] + [L]σ + [Z]η) + ,
240
where β is the per-capita transmission rate, σ is the relative infectivity of the labelled, η is the relative
infectivity of the stigmatized, and is the background infection hazard created by disease reservoirs.
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The instantaneous infection risk for a person is Λdt, and at steady-state, the cumulative probability
that an individual becomes infected over their lifetime (a.k.a. lifetime risk) [LR] = Λ/(Λ + mS ). For
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demographics, people immigrate into the community as susceptible at a known rate, and are removed
from each of the four states at per-capita rates characteristic of their state.
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We can now explore how the rate at which labelled individuals become stigmatized can impact
the prevalence, community size, and life-time risk of infection. Consider three different scenarios
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(see Fig. 2). Scenario 0 (Non-infectious). As a base-scenario, suppose the infection pressure
is independent of the number of those already sick, individuals with the disease die sooner, and
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the disease-state is easily identified in others. Then strong stigmatization rates reduce prevalence
because of the high mortality among the stigmatized. Stigmatization correspondingly reduces the
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population size and is consequently costly to the group (although benefits from selection for disease
resistance may kick-in over longer time scales). Scenario 1 (Pre-Urban). Now, suppose the
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infection pressure is primary from contact with those infected, a community is so small a stigma is
inescapable, stigma increases a person’s mortality risk several fold, and there is no effective medical
treatment or prophylaxis against transmission. Then cultural norms of stigmatization will decrease
13
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prevalence and enlarge a community. Scenario 2 (Modern). But if we are considering a large
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urban community where labelled and stigmatized individuals are diagnosed to receive treatment
which prolongs their lives relative to un-diagnosed individuals, and labelled individuals who have
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not been stigmatized can take prophylactic actions that reduce transmission, while stigmatized
individuals can partially escape ostracism, then stigmatization will increase prevalence and reduce
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community size. Specific parameter values for Scenarios 0, 1, and 2 are given in Table 2.
Comparing Scenarios 0 and 1, we see that the major benefits of stigmatization for a community
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appears only for transmissible diseases. For non-transmissible infections, stigmatization does not
reduce lifetime risk, but does reduce prevalence and population size. Comparison of Scenarios 1
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and 2 shows that the impacts of stigmatization against transmissible diseases are not universally
good or bad, but depend on the specifics of the disease, environment, and medical development of a
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community. These results are consistent with the arguments of Smith and Hughes [14]. The impact
of stigmatization can be summarized by defining a dimensionless stigma ratio Z which represents the
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ratio of the average cumulative transmission of a labelled but unstigmatized individual to the average
cumulative transmission of a stigmatized individual. The relationship between the stigmatization
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rate and the lifetime infection risk ([LR]) is monotone, with the stigma ratio determining the
derivative’s sign – if Z > 1, then more stigmatization decreases lifetime risk, but if Z < 1, then
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more stigmatization increases lifetime risk (see Materials and Methods). The general conditions
for the impact of stigmatization can be obtained through differentiation of the reproductive ratio
276
(see Materials and Methods), and holds in both homogeneous and heterogeneous populations.[TCR:
may need to change]
278
The relative infectiousness of labelled individuals plays a crucial role in determining the impact of
stigmatization (see Fig. 3). If individuals who have been identified as infected receive good medical
280
treatment and counselling, the chance that they further transmit infection can be greatly reduced,
and pre-empt the benefits of stigmatization. On the other hand, if labelled individuals maintain
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relatively high transmission rates, stigmatization remains an effective method of reducing infection
pressure by reducing contact rates. But even in scenarios where more stigmatization reduces the
lifetime infection risk in the community, individuals’ efforts to conceal their disease state because of
14
284
Scenario 0 (Non-infect ious)
100
1.0
Com m unit y size
Prevalence
0.8
Lifet im e Risk
Populat ion
80
60
40
10
-3
10
-2
10
-1
10
0
10
1
10
Scenario 1 (Pre-Urban)
1.0
Lifet im e Risk
Populat ion
60
40
-3
10
-2
10
-1
10
0
10
1
10
2
1
10
2
1
10
2
Scenario 1 (Pre-Urban)
0.6
0.4
0.2
20
10
-3
10
-2
10
-1
10
0
10
1
10
0.0 -4
10
2
Scenario 2 (Modern)
10
-3
10
-2
10
-1
10
0
10
Scenario 2 (Modern)
1.0
10000
0.8
Lifet im e Risk
8000
Populat ion
10
0.8
80
6000
4000
0.6
0.4
0.2
2000
0 -4
10
0.4
0.0 -4
10
2
100
0 -4
10
0.6
0.2
20
0 -4
10
Scenario 0 (Non-infect ious)
10
-3
10
-2
10
-1
10
0
10
1
10
2
Annual rat e of st igm at izat ion (y)
0.0 -4
10
10
-3
10
-2
10
-1
10
0
10
Annual rat e of st igm at izat ion (y)
Figure 2. Comparison of stigma’s impact on prevalence and risk. In Scenario 0 (top),
stigmas applied to a non-transmissible disease reduce both prevalence and community size. In
Scenario 1 (middle), where no treatment is available and stigmatization is inescapable, increasing
rates of stigmatization reduces prevalence and allows for larger communities. In Scenario 2 (bottom),
where treatment is available and stigmatization can be escaped, stigmatization increases prevalence,
leading to reduced community size. See Table 2 for parameter values. Note: stronger stigmas never
increase both community size and prevalence simultaneously.
15
0.8
Prevalence (P)
Lifetime risk of infection (LR)
1.0
0.6
0.4
0.2
0.0 -3
10
10-2
10-1
100
101
102
Annual rate of stigmatization (y)
4000
3500
3000
2500
2000
1500
1000
500
0
10-3
Stigma number
=2.00
=1.50
=1.00
=0.50
=0.02
10-2
10-1
100
101
102
Annual rate of stigmatization (y)
Figure 3. Stigma ratios. As the stigma ratio (Z ) decreases, the benefits of stigmatization are
diminished and reversed. For the lifetime risk [LR], this change occurs exactly when Z = 1.
Prevalence also responses this way, but a smaller value of the stigma ratio is needed before
stigmatization increases prevalence, and the affect of the stigmatization rate may not be monotone
for an intermediate interval of values. Parameters from Scenario 2, but with increasing stigma ratio
corresponding to decreasing relative infectivity of labelled individuals and µZ = 0.06 (Table 2).
fears of stigmatization may diminish and potentially reverse the utility of stigmas. This is called
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“policy resistance” [23], and can be modelled by allowing individuals to change their labelling rate
x to improve their life situation (see Fig. 4) using an objective function calculated with Markov
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decision process theory [24, 25].
4. Discussion
290
Here, we have presented a formal model of the arguments previously made by Smith and Hughes
[14]. Our analysis identifies specific conditions, in terms of the stigma ratio Z , under which the
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stigmas switch from evolutionarily beneficial to detrimental. Our formulas can clarify the growing
rhetorical and policy arguments over the use of stigma as a tool to manage public health in this and
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other health contexts [26]. Rather than falling back on unstated prior beliefs that bias discussions of
stigmatization, the relative merits of stigmatization can now be directly estimated from empirical
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data using the formulas we supply. This will help us move toward an evidence-based dialog about the
reasons for stigmatization and the best approaches available for coping with it and the underlying
infectious disease.
16
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Lifetime risk of infection (LR)
1.0
Labelling rate x =1
1.0
Relative infectivity
of Labelled(σ)
σ =1.00
σ =0.75
σ =0.50
σ =0.25
σ =0.00
0.8
0.6
0.4
0.8
0.6
0.4
0.2
0.0 -3
10
Labelling rate x = xbest(y,ω)
0.2
10-2
10-1
100
101
102
Annual rate of stigmatization (y)
0.0 -3
10
10-2
10-1
100
101
102
Annual rate of stigmatization (y)
Figure 4. Stigma can backfire into policy resistance. In situations like Scenario 1 where
faster stigmatization uniformly leads to lower risk when the labelling rate is fixed (left), cryptically
infected individuals can reverse the benefits of stigmatization by manipulting their labelling rate in
their own self-interest and concealing their infection state (right). In the case shown here, the
population has weakly heterogeneous beliefs about the values of each state. For high relative
infectivity (σ = 1), the community is best off maximizing the stigmatization rate; for low relative
infectivity (σ = 0), the community is best off minimizing stigmatization, and for intermediate
relative infectivity, the best stigmatization rate is about 1/10 per year. Parameters from Scenario 1
(Table 2), with xbest ∈ (1/10, 12) per year.
17
Evolution of the stigma ratio Z from high to low values may well be a marker of a larger
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transition in the modern era, where populations are concentrated in urban areas and while advances
in public health have removed the threats from pestilences like cholera, tuberculosis, smallpox, and
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plague that beset early cities. However, this transition is mediated by the institutional, cultural,
demographic, and Darwinian components of societal evolution, the last two of which progresses more
304
slowly than the first two. The different time-scales create a tension within societies as some people
struggle to reconcile their instincts with reason and social norms. Migrations that bridge gradients in
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social norms between urban and rural communities may add to this tension. Modern outbreaks for
stigmatization in response to new epidemics like HIV [27] and Ebola [28] may well be symptoms of
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this tension – the initially lack ameliorating public health interventions and established social norms
leaves people to revert to instinctual behavioral responses.
310
Of course, our stigma ratio theory does not account for all possibilities. We have not attempted to
directly model the rich variety of events and behaviors that follow stigmatization. To the best of our
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understanding, these can have strong dependences on population composition, culture, environment,
and the particular infectious disease, and further study will be needed to extend our theory beyond
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it’s current scope. Nor have we tried to account for costs associated with the common false-positive
application or conflation of stigmas, or any possible side-effects. And there may well be additional
316
knock-on effects to public health or social structure. For applications, our theory should probably be
extended by merging demographic components of population structure, including age, gender, and
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race.
Our measures of group success have only been group size and lifetime risk, and thus can interpreted
320
under either group selection [29] or cultural [30] theories of community evolution. We have not
attempted to address the more complicated impacts of disease and stigma on group function or
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productivity. Selective pressures for stigmatization may be offset in part by kin-selection in the scope
of family units, that favors nursing and care of sick individuals as a means of improving survival
324
and reproductive success of ones own genes. Infectious disease prevalence can promote sociality
[31]. Such behavior is, in fact, well documented [32], and we may expect further effects to emerge
from larger-scale structures in social networks. However, sometimes kin-relationships accelerate
18
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stigmatization as family members attempt to avoid “courtesy stigma” [9, 10], complicating the matter
328
further.
Our analysis has only considered cases of chronic infectious diseases. While we expect the same
330
factors to be at play in a case of an epidemic of an acute immunizing infection, dynamic aspects of
the epidemic and stigmatization will become very important, as the infection hazards will change
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relatively quickly, ultimately receding entirely, while stigmas may persist long after the epidemic
ends, and have negative impacts on both individuals and communities. In addition, care-giving by
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family members and neighbors may have short-term costs and risks, but long-term benefits which
will compete in decision processes. Our general conclusion should still hold: stigmas will help or
336
hurt individuals and communities, depending on the quality of health care and the effectiveness of
stigmatization at reducing risk. But any benefits are likely to be short term, and to disappear as the
338
epidemic wains. However, scenario-specific analyses will be needed to make sense of all the moving
parts.
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5. Conclusion
In conclusion, we have provided a quantitative theory of how stigmatization of infected individuals
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can affect community health, and shown that while stigmatization may have had benefits historically,
this may well not be the case in dense modern societies. We hope our theory will prove useful in
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futures studies of infectious disease stigmas and will provide a foundation for future mathematical
and computational studies, as well as policy planning.
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6. Acknowledgements
The research was in part supported by National Science Foundation grant CCF-12156822 (TR),
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and the National Human Genome Research Institute of the National Institutes of Health under
Award Number R21HG007111 (RS).
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