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RESEARCH ARTICLE
Internal and external factors affecting
vaccination coverage: Modeling the
interactions between vaccine hesitancy,
accessibility, and mandates
Kerri-Ann M. Anderson, Nicole CreanzaID*
Department of Biological Sciences and Evolutionary Studies Initiative, Vanderbilt University, Nashville,
Tennessee, United States of America
*nicole.creanza@vanderbilt.edu
Abstract
Society, culture, and individual motivations affect human decisions regarding their health
behaviors and preventative care, and health-related perceptions and behaviors can change
at the population level as cultures evolve. An increase in vaccine hesitancy, an individual
mindset informed within a cultural context, has resulted in a decrease in vaccination cover-
age and an increase in vaccine-preventable disease (VPD) outbreaks, particularly in devel-
oped countries where vaccination rates are generally high. Understanding local vaccination
cultures, which evolve through an interaction between beliefs and behaviors and are influ-
enced by the broader cultural landscape, is critical to fostering public health. Vaccine man-
dates and vaccine inaccessibility are two external factors that interact with individual beliefs
to affect vaccine-related behaviors. To better understand the population dynamics of vac-
cine hesitancy, it is important to study how these external factors could shape a population’s
vaccination decisions and affect the broader health culture. Using a mathematical model of
cultural evolution, we explore the effects of vaccine mandates, vaccine inaccessibility, and
varying cultural selection trajectories on a population’s level of vaccine hesitancy and vacci-
nation behavior. We show that vaccine mandates can lead to a phenomenon in which high
vaccine hesitancy co-occurs with high vaccination coverage, and that high vaccine confi-
dence can be maintained even in areas where access to vaccines is limited.
Introduction
A comprehensive understanding of health behaviors and their potential for exacerbating or
mitigating disease risk requires insight into how cultural beliefs influence these behaviors.
Local vaccination cultures—the shared beliefs among individuals within a community about
vaccine-preventable disease etiology, prevention, and treatment—can affect an individual’s
vaccine attitudes and decisions [1,2]. The definition of “vaccine hesitancy” varies between
sources, spanning from an attitude of uncertainty about vaccines to the behavior of vaccine
refusal. Here we use the definition from Larson et al. 2022 [3]: “a state of indecision and
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OPEN ACCESS
Citation: Anderson K-AM, Creanza N (2023)
Internal and external factors affecting vaccination
coverage: Modeling the interactions between
vaccine hesitancy, accessibility, and mandates.
PLOS Glob Public Health 3(10): e0001186. https://
doi.org/10.1371/journal.pgph.0001186
Editor: Julia Robinson, PLOS: Public Library of
Science, UNITED STATES
Received: May 31, 2022
Accepted: August 22, 2023
Published: October 4, 2023
Copyright: ©2023 Anderson, Creanza. This is an
open access article distributed under the terms of
the Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Data Availability Statement: All code for the
mathematical model is available in a public GitHub
repository at https://github.com/CreanzaLab/
Vaccine-Hesitancy and in a permanent repository
on Figshare (doi.org/10.6084/m9.figshare.
22493317).
Funding: K-A.M.A. and N.C. are supported by
Vanderbilt University and the John Templeton
Foundation. The funders had no role in study
design, data collection and analysis, decision to
publish, or preparation of the manuscript.
uncertainty that precedes a decision to become (or not become) vaccinated.” In 2019, vaccine
hesitancy was named one of the World Health Organization’s ten threats to global health [4]
because of its link to reduced vaccination coverage and more frequent outbreaks of vaccine-
preventable diseases (VPDs) worldwide. Vaccine hesitancy is a key indicator of the vaccination
culture of a population, and public health studies have considered vaccine hesitancy to be
influenced by multiple societal- and individual-level factors, such as the vaccination coverage
of the population, the perceived risk of vaccine-preventable diseases, the level of trust in spe-
cific vaccines, and the confidence in the healthcare system (e.g. [5–7]). Modeling studies have
incorporated a subset of these factors [8], such as vaccination coverage [9] and perceived dis-
ease risk [10].
More broadly, theoretical studies have modeled how the spread of disease can be affected
by aspects of human behavior, particularly vaccination and social distancing behaviors [8,11–
16]. Other models have examined a phenomenon known as “coupled contagion,” in which
individuals can transmit not only a disease itself but also cultural factors such as vaccine adop-
tion, disease-related fears, and (mis)information, which can in turn modulate their disease sus-
ceptibility in the simulation [10,17–19]. In real populations, health policies and other external
factors can play a role in shaping vaccination cultures; two such factors are vaccine mandates,
which drive vaccination uptake (even among vaccine-hesitant people), and vaccine inaccessi-
bility, which hinders vaccine uptake (even among vaccine-confident people). Vaccine man-
dates have been met with opposition since their implementation in the 1800’s [20,21]. This
opposition, intertwined with religious and political ideas, led to the allowance of vaccination
exemptions based on medical and non-medical (e.g. religious or philosophical) reasons [22].
Though the implementation of mandatory vaccinations generally results in a drastic reduction
in disease incidence and mortality [23,24], the high vaccination coverage that follows can
facilitate the public perception of reduced disease severity and thus reduced vaccine necessity;
this phenomenon has been observed in real populations [25,26] and incorporated into model-
ing studies [2,8,27]. In this vein, non-medical exemptions to mandatory vaccination have
been increasing, particularly in wealthier countries where theoretical predictions suggest that
belief systems can act as the main barrier to vaccination, as opposed to lack of vaccine access
[28,29]. This rise in non-medical exemptions appears to have a non-trivial effect on public
health, since these exemptions are correlated with the recent increase in VPD outbreaks in the
United States [30,31]. However, the circumstances under which vaccine mandates might lead
to increased vaccine hesitancy remain uncertain.
Even less understood is the potential association between vaccine (in)accessibility and vac-
cine attitudes. Vaccine accessibility issues are external pressures that negatively impact vacci-
nation rates and coverage. Challenges to vaccine accessibility are particularly prevalent in low
and middle-income countries as well as rural areas in developed countries [32,33]. For exam-
ple, storage capabilities, distribution logistics, and affordability can limit the number of vaccine
doses available in a specific area, and thus reduce the number of individuals who can receive a
vaccine, leaving vulnerable communities at risk for a VPD outbreaks [32,34]. External factors
such as limited vaccine access and vaccine mandate policies may also interact with internal fac-
tors like psychological characteristics and cultural predispositions, such as distrust in the
healthcare system, potentially exacerbating the effects of low vaccine accessibility. Further, vac-
cination cultures can be shaped by experience with vaccines and with the disease: for example,
living in a rural area could limit exposure to the disease and alter the perception of disease risk,
and a lack of vaccine access for an extended period could entrench certain attitudes about vac-
cines in a culture. Thus, to explain the differences in vaccination outcomes and resulting dis-
ease risk across human populations, it is crucial to better understand how cultural beliefs and
behaviors interact with external pressures that increase or reduce vaccination coverage.
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Competing interests: The authors have declared
that no competing interests exist.
Cultural niche construction theory describes a process in which humans modify their cultural
environments—for example, their beliefs, behaviors, preferences, and social contacts—in ways
that subsequently alter evolutionary pressures on the population and its culture [35]. Mathemati-
cal models of cultural niche construction have been used to explain the evolution of behaviors
related to religion, fertility, and large-scale human conflict [35–40]. Since health cultures can be
shaped by or influence the larger cultural landscape, the cultural niche construction framing can
give insight into the cultural dynamics shaping disease risk. By using this type of model to simu-
late the interactions between beliefs and behaviors, we seek to understand how vaccination cul-
tures affect vaccination coverage, as well as how vaccine-related beliefs and behaviors are affected
by external forces, such as the availability of vaccines and the degree to which they are mandatory.
We adapted a cultural niche construction framework to model vaccination beliefs and
behaviors, incorporating the transmission of vaccination culture both from parents and from
the community [9], and we used current estimates of vaccination rates and vaccine attitude
frequencies obtained from various sources in the literature, including reports of Measles-
Mumps-Rubella uptake from the United States [41,42], as a starting point our model. Using
this model, we previously demonstrated that the overarching cultural landscape, including the
likelihood of adopting vaccine hesitancy and the probability of transmitting it to one’s chil-
dren, determines the equilibrium levels of vaccination coverage and vaccine hesitancy in a
population. In addition, we demonstrated that the transmission of vaccine confidence and
positive vaccine perception are imperative to maintaining high levels of vaccination coverage,
especially when individuals preferentially choose a partner with shared vaccine beliefs. In this
manuscript, we expand the scope of this model to explore how the vaccination coverage and
vaccine hesitancy in a population could be affected by external forces. In particular, we focus
on vaccine mandates and vaccine inaccessibility, which both lead to a decoupling of parental
vaccine beliefs and their vaccination behaviors, such that vaccine mandates can increase the
chances that vaccine-hesitant parents will vaccinate their children, and vaccine inaccessibility
can decrease the chances that vaccine-confident parents will vaccinate their children. We
quantify the population-level differences predicted by our model for populations with vaccine
mandates or vaccine inaccessibility compared to a baseline population with accessible and
non-mandated vaccines. Overall, we explore the effects of these external forces on the dynam-
ics of both vaccine beliefs and vaccination coverage, providing insight into the differences
between cultural development in the opposing contexts of mandates and inaccessibility.
Methods
We build on a more general cultural niche construction framework of [9,39] to assess the
effects of two external factors, vaccine mandates and vaccine accessibility, on the resulting
landscape of vaccination coverage and vaccine confidence. For a population of individuals, we
track the status of vaccination coverage and vaccine confidence over time; within this popula-
tion, individuals mate, decide whether to vaccinate their offspring, and transmit a vaccine atti-
tude trait. Their decision to vaccinate is influenced by their own beliefs and their vaccination
states, and population trait frequencies are further modulated by vaccination-frequency-
dependent cultural selection pressures. To model the effects of the external factors, we assume
that vaccine mandates and inaccessibility both act to reduce the influence that internal factors,
such as individual beliefs, have on vaccination behaviors.
General framework of the model
Each individual in our model (depicted in Fig 1) has a vaccination (V) trait, either V
+
(vacci-
nated) or V
−
(unvaccinated), and an attitude (A) trait, either A
+
(vaccine confident) or A
−
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(vaccine hesitant), resulting in four possible phenotypes (V
+
A
+
, V
+
A
−
, V
−
A
+
, and V
−
A
−
) that
we initialize with frequencies structured to represent those of the United States: V
+
A
+
(i.e. fre-
quency of vaccinated, vaccine confident individuals) = 0.81, V
+
A
−
= 0.1, V
−
A
+
= 0.07, V
−
A
−
=
0.02. These frequencies were estimated using reports of Measles-Mumps-Rubella vaccination
rates and estimates of vaccine attitude frequencies obtained from various sources in the litera-
ture [41,42]. In each iteration, individuals mate randomly within the population. Each paren-
tal pair vaccinates their offspring with probability B
m,n
(i.e., vertical transmission of
vaccination, with the subscript mdenoting the vaccination trait pair and ndenoting the atti-
tude trait pair of the parents; see Table 1 and S1 Table); in general, this probability increases
with each vaccinated and vaccine-confident parent. This vaccination probability is influenced
by two factors: whether each of the parents are themselves vaccinated (b
m
), and whether each
of the parents are vaccine confident or hesitant (c
n
). The probability that a couple vaccinates
their offspring is calculated as Bm;n¼cn
1þbm
2
�, to account for the influence of both vaccination
states and vaccine attitudes. We model varying levels of vaccine mandates and inaccessibility
by modulating the influence that parental vaccine attitudes have on the likelihood that they
vaccinate their offspring (by increasing or decreasing c
n
): for example, a vaccine mandate will
make a vaccine-hesitant parent more likely to vaccinate their child, and vaccine inaccessibility
will make a vaccine-confident parent less likely to vaccinate their child.
Each parental pair also transmits a vaccine attitude trait to their offspring (i.e., vertical
transmission of beliefs) with vaccine confidence transmitted at probability C
n
and vaccine hes-
itancy at probability 1-C
n
. We set the probability of transmitting vaccine confidence to be
highest for two vaccine-confident parents and lowest for two vaccine-hesitant parents
(Table 1). For simplicity, we set the baseline confidence transmission probabilities (C
n
) to
Fig 1. Workflow of a single iteration of the model. The schematic shows the processes within a single model iteration. The model is initialized with
the phenotypic frequencies (V
+
A
+
, V
+
A
−
, V
−
A
+
, V
−
A
−
) in the population. After individuals mate and reproduce, they vertically transmit vaccination
and attitude traits to their offspring. Vaccination trait frequencies are further modulated by cultural selection. Oblique transmission (cultural
transmission from non-parental adults in the population) follows, which may lead offspring to alter their attitude state. (Parameters, their definitions,
and baseline values are listed in Table 1).
https://doi.org/10.1371/journal.pgph.0001186.g001
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values reminiscent of Mendelian transmission, such that two vaccine-confident or two vac-
cine-hesitant parents predictably (~100% likely) transmit their vaccine attitude, and parents
with differing vaccine attitudes each have a ~50% chance of transmitting each state: C
0
near 0,
C
1
and C
2
at 0.5, C
3
near 1 (Table 1). Influence parameters, b
m
and c
n
, are valued similarly and
predict the probability that the couple vaccinates their children according to the equation
Bm;n¼cn
1þbm
2
�such that parents who are both vaccine confident and vaccinated are most
likely to vaccinate, vaccine hesitant and unvaccinated parents are least likely to vaccinate, and
parental pairs with mixed states of one or both traits will have intermediate likelihoods of
vaccinating.
Each parental pair also transmits a vaccine attitude trait to their offspring (i.e., vertical
transmission of beliefs) with vaccine confidence transmitted at probability C
n
and vaccine hes-
itancy at probability 1-C
n
. We set the probability of transmitting vaccine confidence to be
highest for two vaccine-confident parents and lowest for two vaccine-hesitant parents
(Table 1). For simplicity, we set the baseline confidence transmission probabilities (C
n
) to val-
ues reminiscent of Mendelian transmission, such that two vaccine-confident or two vaccine-
hesitant parents predictably (~100% likely) transmit their vaccine attitude, and parents with
differing vaccine attitudes each have a ~50% chance of transmitting each state: C
0
near 0, C
1
and C
2
at 0.5, C
3
near 1 (Table 1). Influence parameters, b
m
and c
n
, are valued similarly and
predict the probability that the couple vaccinates their children according to the equation
Bm;n¼cn
1þbm
2
�, such that parents who are both vaccine confident and vaccinated are most
likely to vaccinate, vaccine hesitant and unvaccinated parents are least likely to vaccinate, and
parental pairs with mixed states of one or both traits will have intermediate likelihoods of
vaccinating.
Next, cultural selection (σ; -1 �σ�1) operates on the resulting phenotype frequencies
such that the frequency of vaccination in the population is greater or less than expected given
the predicted probabilities that vaccine-confident and -hesitant parents vaccinate their off-
spring. The proportion of vaccinated individuals in the population is multiplied by 1+σ, such
that a positive σincreases the proportion of vaccinated individuals and a negative σdecreases
Table 1. List of parameters, their definitions, and baseline values.
Parameter Meaning Baseline values (if
applicable)
VVaccination state (V
+
vaccinated, V
−
unvaccinated)
AVaccine attitude (A
+
confident, A
−
hesitant)
mand nParameter subscripts indicating traits of the mating pair (in b
m
,c
n
,C
n
, and
B
m,n
)
V
−
×V
−
:m= 0; V
−
×V
+
:m= 1; V
+
×V
−
:m= 2; V
+
×V
+
:m= 3
A
−
×A
−
:n= 0; A
−
×A
+
:n= 1; A
+
×A
−
:n= 2; A
+
×A
+
:n= 3
B
m,n
Probability that parental pairs vaccinate their children, which depends
upon the parents’ vaccination states (b
m
) and vaccine attitudes (c
n
) (given
in S2 Table)
C
n
Probability that parental pairs transmit vaccine confidence to their children C
0
= 0.01, C
1
=C
2
= 0.5,
C
3
= 0.99
b
m
Probability that parental pairs support offspring vaccination given their
vaccination states
b
0
= 0.01, b
1
=b
2
= 0.5,
b
3
= 0.99
c
n
Probability that parental pairs support offspring vaccination given their
vaccine attitude
c
0
= 0.01, c
1
=c
2
= 0.5, c
3
= 0.99
σComprehensive selection coefficient for V
+
, dependent on the population-
wide vaccination rate (see S1 Fig)
σ
max
The highest additional benefit that can be conferred by vaccination σ
max
= 0.1
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it. This process encompasses the various factors that might make parents more or less likely to
vaccinate, including the severity of the disease and the general trust in the healthcare system.
Since the perceived benefit of the vaccine might vary based on the vaccination coverage in the
population, we allow σto depend on the frequency of the V
+
trait: when the frequency of vacci-
nation is low, the effects of the disease are more evident and individuals are more likely to vac-
cinate (high σ), but when the frequency of vaccination is high, the risks of the disease are
masked and individuals are less likely to vaccinate (lower σ) (see S1 Text for a more detailed
explanation of how σis calculated as a function of vaccination coverage (V
+
)). The equation
relating the frequency of V
+
and σis given in S1 Fig. In genetics, the selection coefficient is tra-
ditionally small (in the range of -0.1 to 0.1 [43]); at baseline in our model, we kept the maxi-
mum cultural selection coefficient at 0.1 which allowed for both positive and negative selection
depending on the frequency of vaccinated individuals in the previous iteration.
Finally, oblique interactions (cultural influences from non-parental individuals) then act to
further modify trait frequencies in the population. Individuals in the simulation can change
their vaccine attitudes based on interactions with others and their perceptions of their sur-
roundings. If the vaccination coverage in the population is low, we consider the negative
effects of the disease to be more apparent and thus people will be less likely to adopt a vaccine-
hesitant attitude, and if the vaccination coverage is high, the negative effects of the disease are
prevented (amplifying the perception of the vaccine’s risks and costs, however small) and peo-
ple might be more likely to become vaccine hesitant (S2 Fig). Each subsequent iteration of the
model begins with the phenotype frequencies produced at the end of the current iteration. The
simulation is run until phenotype frequencies reach equilibrium (Fig 1,Table 1). For more
detail see S1 Text and [9]. The code for the simulations is written in MATLAB and is provided
at www.github.com/CreanzaLab/Vaccine-Hesitancy and http://doi.org/10.6084/m9.figshare.
22493317.
Parameterization for mandatory vaccination and vaccine inaccessibility
simulations
We hypothesize that parental vaccine attitudes influence their use of exemptions and thus lev-
els of non-vaccination will differ based on parental attitudes under a mandated vaccination
system. Therefore, we simulate the effects of mandatory vaccination by modulating the influ-
ence of a couple’s vaccine attitudes on their likelihood of vaccinating their offspring (c
n
); in
other words, a vaccine mandate alters the influence of a couple’s vaccine attitude on their deci-
sion to vaccinate. We assume the implementation of mandates would increase vaccination in
couples with at least one vaccine-hesitant individual. If vaccination exemptions are permitted,
we expect that A
−
×A
−
couples (those with two vaccine-hesitant individuals) would be most
likely to obtain exemptions, followed by mixed attitude (A
−
×A
+
or A
+
×A
−
) couples, with
vaccine confident couples (A
+
×A
+
) being least likely. Hence, to model the effects of imple-
menting a vaccine mandate, we increase attitude influence parameters from baseline values
(Table 1) to represent two levels of mandate strictness, a strict mandate in which c
0
= 0.5, c
1
=
c
2
= 0.9, c
3
= 0.99 and a less strict mandate in which c
0
= 0.3, c
1
=c
2
= 0.7, c
3
= 0.99.
Similarly, to represent a vaccine inaccessibility scenario, we reduced the influence of paren-
tal vaccine attitudes on vaccination behaviors for couples with at least one confident individual
(i.e. reducing c
1
,c
2
,c
3
from baseline values). In this simple representation of a vaccine-scarce
environment, we assume that parents’ confidence in vaccines would have reduced influence
on their ability to vaccinate their offspring, that is, their vaccine confidence does not ensure
their ability to overcome vaccine inaccessibility. Hesitant couples are least likely to vaccinate
their offspring regardless of vaccine availability, but couples who would likely vaccinate their
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Modeling the interactions between vaccine hesitancy, accessibility, and mandates
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offspring given the chance would have difficulty doing so due to the lack of access. We mod-
eled two levels of vaccine inaccessibility–a somewhat inaccessible vaccine in which c
0
= 0.01, c
1
=c
2
= 0.3, and c
3
= 0.7 and an inaccessible vaccine in which c
0
= 0.01, c
1
=c
2
= 0.1, c
3
= 0.5.
Assuming mixed attitude (A
−
×A
+
or A
+
×A
−
) couples exhibit the most variability in their
likelihood of transmitting vaccine confidence, we then examined the effect of the interaction
between the maximum cultural selection coefficient (σ
max
) and mixed-attitude confidence
transmission probability (C
1
=C
2
) for a scenario with baseline parameters (no active mandate
and an accessible vaccine), with a less strict mandate, and with a somewhat inaccessible
vaccine.
We next examined the effects of varying the transmission probability of vaccine confidence
parameters for all couple types (C
0
,C
1
,C
2
and C
3
), instead of focusing on the vaccine confi-
dence transmission of mixed-attitude couples. We varied all C
n
parameters simultaneously
within a specified range of values (S3 Table) across different levels of mandate strictness and
vaccine inaccessibility. As before, we varied these parameters in conjunction with the maxi-
mum cultural selection coefficient σ
max
.
Results
Mandatory vaccination and vaccine inaccessibility
We examined the effect of the interaction between the maximum cultural selection coefficient
(σ
max
) and confidence transmission probability of mixed-attitude couples (A
−
×A
+
and A
+
×
A
–
;C
1
=C
2
) (Fig 2). Modeling the effects of a vaccine mandate reveals a decoupling of vaccina-
tion coverage and vaccine confidence trajectories when parents are more likely to transmit
vaccine hesitancy (Fig 2C and 2D). Even when vaccine confidence is very low (specifically at
mixed-trait couple confidence transmission probabilities below 0.5; red region in Fig 2D), vac-
cination coverage is higher with a less strict mandate implemented than without a mandate
(compare Fig 2C and 2D to Fig 2A and 2B;S4 Table). However, the leniency of the mandate in
Fig 2C and 2D means that many vaccine-hesitant couples can obtain an exemption, and vacci-
nation coverage remains lower when vaccine hesitancy is common. This suggests that an exter-
nal pressure to vaccinate helps overcome the opposing cultural pressure imposed by hesitancy
in the population, but a mandate would have to be stricter to achieve herd immunity in a pre-
dominantly vaccine-hesitant population.
When vaccines were somewhat inaccessible, vaccination coverage was noticeably reduced
overall, while vaccine confidence increased slightly across the parameter space. Juxtaposed
with the mandate scenario (Fig 2C and 2D), our vaccine scarcity models produce an opposite
deviation of vaccination coverage from vaccine confidence levels: when vaccines are man-
dated, we observe increased vaccination coverage in low-confidence environments, and when
vaccines are inaccessible, we observe lower than expected vaccination coverage (<50%) in a
predominantly vaccine-confident environment (>90%) (Fig 2).
Mandatory vaccination may increase vaccination coverage at the expense of
confidence, while vaccine inaccessibility promotes confidence
In the three scenarios examined thus far—baseline (no mandate and accessible vaccines), a less
strict mandate, and somewhat inaccessible vaccines—most of the variability in equilibrium fre-
quencies across the parameter space occurs at confidence transmission levels between C
1
=C
2
= 0.4 to 0.6 (Fig 2). This threshold region separates definitively higher and definitively lower
vaccination coverage and vaccine confidence outcomes. The effect of actual and perceived vac-
cine fitness (σ) is also most noticeable in this region of the heatmap: as cultural selection for
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vaccination increases at any fixed probability of confidence transmission, vaccination coverage
and vaccine confidence levels at equilibrium are increased. Changes in vaccination and confi-
dence frequencies are not independent of each other, as these effects are the consequence of
changes in phenotypic frequencies. Therefore, for each scenario, we plotted the temporal
dynamics of each phenotype (VA) and the vaccination (V
+
) and confidence (A
+
) traits at base-
line parameter values (Fig 3), then calculated the difference in frequency from baseline equilib-
rium (Fig 4). With an accessible vaccine that is not mandated (Figs 3A and 4), the phenotype
frequencies of the system equilibrate generally with either vaccinated and vaccine confident
(V
+
A
+
) or unvaccinated and vaccine hesitant (V
–
A
–
) individuals most abundant (Figs 3A and
4). Though these two phenotypes remain the most abundant when a less strict vaccine man-
date is implemented, the equilibrium frequency of vaccinated but vaccine-hesitant individuals
(V
+
A
–
) is greatly increased compared to baseline (Figs 3B and 4). Interestingly, a mandate also
results in a higher frequency of unvaccinated and vaccine-hesitant individuals (V
–
A
–
), while
Fig 2. External factors (vaccine mandates and vaccine scarcity) decouple equilibrium levels of vaccine confidence from vaccination coverage.
Heatmaps showing equilibrium vaccine coverage and vaccine confidence levels with an accessible vaccine and no active mandate (A, B), with an
accessible vaccine and a less strict mandate (C, D) and an environment with vaccines somewhat inaccessible (E, F). Assuming mixed-attitude couples
might have the most variability in their likelihood of transmitting vaccine confidence to their offspring, we vary C
1
=C
2
(confidence transmission
probability of mixed-attitude couples) on the vertical axis, and maximum selection coefficient σ
max
(indicative of the perceived value of vaccinating
offspring) on the horizontal axis. A less strict mandate (C, D) is modeled by c
0
= 0.3, c
1
=c
2
= 0.7, c
3
= 0.99; vaccine inaccessibility (E, F) is modeled by
c
0
= 0.01, c
1
=c
2
= 0.3, c
3
= 0.7. Unspecified parameters are given in Table 1. These simulations show an inverse correlation between vaccination
coverage and vaccine confidence at C
n
<0.5 under a less strict mandate, and C
n
>0.5 when vaccine access is limited. Baseline conditions (Table 1) are
highlighted by black boxes in each heatmap. To facilitate comparisons between panels, the mean and median for the section of the heatmaps with C
1
=
C
2
<0.5 are presented in S4 Table.
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reducing vaccinated and vaccine-confident individuals (V
+
A
+
) in the population. Vaccine
inaccessibility, on the other hand, resulted in approximately double the frequency of unvacci-
nated but vaccine-hesitant (V
–
A
+
) individuals. In summary, compared to baseline outcomes,
implementation of a mandate increases vaccination coverage at the expense of confidence by
driving vaccination in hesitant individuals, and vaccine inaccessibility promotes confidence
despite low vaccination coverage by driving confidence in unvaccinated individuals.
Vaccination and confidence frequencies are more variable when offspring
beliefs are more likely to differ from their parents’ beliefs
The clear disjunction between higher and lower vaccination (V
+
) and vaccine confidence (A
+
)
frequencies observed in Fig 2 is not observed when the probability of confidence transmission
Fig 3. Vaccine mandates and inaccessibility drive different distributions of both vaccination coverage and vaccine confidence. Phenotype and trait
frequencies are plotted over 100 model iterations. Compared to baseline transmission levels (panel A, parameter values given in Table 1), a less strict
vaccine mandate (c
0
= 0.3, c
1
=c
2
= 0.7, c
3
= 0.99; panel B) leads to increased vaccination coverage at equilibrium (black line) but decreased vaccine
confidence levels (magenta line). In contrast, when a vaccine is somewhat difficult to access (c
0
= 0.01, c
1
=c
2
= 0.3, and c
3
= 0.7; panel C), vaccination
coverage is lower than in panel Abut vaccine confidence is higher. The specific simulations shown here are highlighted with black rectangles on the
heatmaps in Fig 2.
https://doi.org/10.1371/journal.pgph.0001186.g003
Fig 4. Change from baseline equilibrium frequencies. Final equilibrium frequencies for baseline, a less strict vaccine mandate, and a somewhat
inaccessible vaccine are shown along with the percent difference from baseline frequencies. Colored lines in the first row correspond to the line colors
in Fig 3. Negative changes are indicated by a red downward pointing triangle; positive changes are indicated by green upward pointing triangle. A
vaccine mandate leads to increased vaccination among vaccine-hesitant individuals, and vaccine inaccessibility leads to decreased vaccination and
increased vaccine confidence among unvaccinated individuals.
https://doi.org/10.1371/journal.pgph.0001186.g004
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Modeling the interactions between vaccine hesitancy, accessibility, and mandates
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is modulated for all couples (Fig 5). When mixed-attitude couples transmit confidence to their
offspring at high (C
1
=C
2
>0.5) or low (C
1
=C
2
<0.4) probabilities, which skews population
attitude frequencies to either highly confident or highly hesitant, the subsequent offspring are
more likely to vaccinate (in a confident population) or not vaccinate (in a hesitant population)
(Fig 2). Similarly, if all couple types are transmitting confidence at lower probabilities or higher
probabilities (i.e. C
0
,C
1
,C
2
, and C
3
are all lower or higher, respectively), vaccination frequen-
cies will equilibrate at either lower levels or higher levels (Fig 5). However, if all couples are
transmitting confidence at mid-range probabilities (or C
1
and C
2
are closer to 0.5), the popula-
tion equilibrates at more polymorphic frequencies, that is, both forms of each trait coexist in
the population at moderate frequencies.
Equilibrium vaccination coverage increases as cultural selection for vaccination increases in
both mandated vaccines (Fig 5C and 5E) and vaccine inaccessibility scenarios (Fig 6C and 6E);
confidence frequencies remain more consistent across the range of cultural selection pressures
(Figs 5D, 5F,6D and 6F). When we model an increase in vaccine mandate strictness (increased
difficulty in obtaining exemptions), vaccination frequencies are increased (Fig 5C and 5E). On
the other hand, greater degrees of inaccessibility lead to larger reductions in vaccination cover-
age (Fig 6C and 6E), and lower coverage occurs despite higher levels of vaccine confidence.
Fig 5. Increasing mandate strictness and increased cultural selection drive vaccination coverage. Heatmaps showing final vaccination coverage (A,
C, E) and corresponding vaccine confidence (B, D, F) after 100 time-steps while simultaneously varying all confidence transmission probabilities (C
n
;
vertical axis) and maximum selection coefficient (σ
max
; horizontal axis). We show an accessible vaccine with no mandate (c
0
= 0.01, c
1
=c
2
= 0.5, c
3
=
0.99) (A, B), a less strict mandate (c
0
= 0.3, c
1
=c
2
= 0.7, c
3
= 0.99) (C, D), and a strict mandate (c
0
= 0.5, c
1
=c
2
= 0.9, c
3
= 0.99) (E,F). C
n
values are set
within the range indicated on the vertical axis with C
0
taking the lowest value, C
1
and C
2
taking intermediate values, and C
3
taking the highest value (S3
Table).
https://doi.org/10.1371/journal.pgph.0001186.g005
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Modeling the interactions between vaccine hesitancy, accessibility, and mandates
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Changing the relationship between vaccination coverage and cultural
selection can alter vaccination behavior when the vaccine is accessible
In the previous analyses, we assumed that the cultural selection for vaccination would begin to
decrease from its maximum value as members of a population with widespread vaccination
coverage (exceeding 70% vaccination coverage, see S1 Fig) might perceive a reduced cost of
the disease and thus a reduced pressure to vaccinate their children. To assess the robustness of
our model to different relationships between vaccination coverage and cultural selection pres-
sures, for example representing variations in herd immunity criteria or in parent priorities, we
tested the same simulations with multiple cultural selection functions. We examined the inter-
action between mixed-attitude pair confidence transmission probability (C
1
=C
2
) and a range
of maximum cultural selection coefficients (σ
max
) for these different cultural selection func-
tions (shown in S3A Fig for σ
max
= 0.1). In line with cultural selection acting primarily on the
vaccination trait, most of the differences among the cultural selection functions are observed
in the vaccination equilibrium frequencies and not the confidence equilibrium frequencies,
particularly when no mandates or less strict mandates are imposed (S3B and S3C Fig). Com-
pared to the baseline function used in Figs 2,3,5and 6(also shown in S3 Fig,column 3),
Fig 6. Vaccine inaccessibility reduces vaccination coverage despite high levels of vaccine confidence. Heatmaps showing final vaccination coverage
(A, C, E) and corresponding vaccine confidence (B, D, F) after 100 time-steps while simultaneously varying all confidence transmission probabilities
(C
n
; vertical axis) and maximum selection coefficient (σ
max
; horizontal axis). C
n
values are set within the range indicated on the vertical axis with C
0
taking the lowest value, C
1
and C
2
taking intermediate values, and C
3
taking the highest value (S3 Table). We simulate an accessible vaccine and no
mandate (c
0
= 0.01, c
1
=c
2
= 0.5, c
3
= 0.99) (A, B), a somewhat inaccessible vaccine (c
0
= 0.01, c
1
=c
2
= 0.3, and c
3
= 0.7) (C, D) and an inaccessible
vaccine (c
0
= 0.01, c
1
=c
2
= 0.1, c
3
= 0.5) (E,F).
https://doi.org/10.1371/journal.pgph.0001186.g006
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when we define “herd immunity” as being achieved at a reduced vaccination coverage level
(corresponding to when σbegins to decrease), vaccination coverage is reduced most noticeably
at the intersection of low values of σ
max
and high values of mixed-attitude pair confidence
transmission (S3B and S3C Fig,column 4). When the level required for herd immunity is
increased, vaccination coverage is increased in this low σ
max
high confidence transmission
area of the heatmap (S3B and S3C Fig,column 2). The overall patterns we observed with the
original cultural selection function are robust to the particular function we used. At higher val-
ues of C
1
=C
2
and σ
max
(top right corner of the heat maps), vaccination coverage was reduced
when the σfunction was more negatively correlated with vaccination coverage (columns 3
through 6 in S3 Fig). In addition, we observed that the largest differences in vaccine coverage
between cultural selection (σ) functions occurred when vaccines were accessible and there
were no mandates (S3B Fig); differences in the cultural selection function had less of an effect
on vaccination coverage when a less strict mandate was imposed (S3C Fig), and had little effect
on vaccination coverage when vaccines were inaccessible (S3D Fig). The least variation is
observed when vaccines are inaccessible: across confidence frequencies, the cultural selection
function did not meaningfully alter the equilibrium vaccination coverage or vaccine confi-
dence (S3D Fig). This result is intuitive, since most differences between cultural selection func-
tions occur in regions of high vaccination coverage, and the simulations with inaccessible
vaccines do not lead to high vaccination coverage for any parameter combination.
Discussion
Here, we build on the cultural niche construction framework proposed by [9] to model the cul-
tural spread of vaccine attitudes and vaccination behavior in the presence of external forces
imposed by two scenarios: vaccine mandates and vaccine inaccessibility. Multiple factors influ-
ence an individual’s vaccine-related beliefs and a couple’s decision to vaccinate their offspring,
including their own vaccination status and their perception of the relative risks of the disease
and the vaccine. As such, it is important that we understand how public health policies, such
as vaccine mandates and barriers to vaccination, such as geography or affordability, can shape
vaccination cultures and thus affect public health. Using a cultural niche construction
approach allows us to explore the effects of the interplay between external forces and cultural
factors providing further insight into how vaccination cultures are formed, maintained, and
evolve.
With our initial model [9], we showed that when population traits are at or near an equilib-
rium, we can infer that a population with high vaccination coverage will have low rates of vac-
cine hesitancy and vice versa. However, when there are external pressures as modeled here,
such as increased pressure to vaccinate or difficulty in acquiring vaccination exemptions, an
undercurrent of vaccine hesitancy can persist in a relatively well-vaccinated population, poten-
tially limiting the adoption of newly introduced vaccines. This possibly contributes to the
unexpected lag in uptake of newer vaccines, such as the COVID or HPV vaccines, in commu-
nities with otherwise high vaccination rates [44–46]. The perceived increase in hesitancy sur-
rounding new vaccines may actually be existing vaccine hesitancy becoming apparent. In
addition, “fence sitters”, those who have not made a firm stance regarding vaccines and thus
could be more influenced by targeted campaigns [42], may develop higher levels of uncertainty
about new vaccines than their parents had about existing ones.
In contrast to the effect of vaccine mandates, by modeling vaccine inaccessibility we illus-
trate another important pattern: reduced vaccination coverage in a vaccine-confident culture.
In a vaccine-scarce environment, an individual’s attitude regarding vaccines has less influence
on vaccination behavior due to the barrier imposed by resource availability. As a result, a
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Modeling the interactions between vaccine hesitancy, accessibility, and mandates
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population may be undervaccinated despite holding vaccine-affirming beliefs. In addition, a
health culture previously shaped by vaccine inaccessibility could potentially ingrain specific
behavioral practices (for example, visiting the doctor only when a child is sick and not for a
regular vaccine schedule) that are not easily modified even if vaccines become more readily
available. These vaccine scarcity scenarios are most likely to exist in low- and middle-income
countries in which vaccine acquisition, storage and/or distribution resources are insufficient
[47–49] whereas the opposite scenario (low vaccine confidence–high vaccination coverage)
after vaccine mandates is most common in developed nations [50]. In summary, we find that
vaccine mandates can result in high vaccination coverage even in a culture of hesitancy, and
that lack of access to vaccines can produce the inverse: low vaccination coverage in a culture of
confidence.
It is difficult, as with any system, to fully capture the complex reality of vaccine hesitancy
and vaccination behavior with a mathematical model. Caveats of this model include the lack of
empirical data to inform how we model the influence of vaccine confidence on vaccination
behaviors in the face of mandates or vaccine inaccessibility. A potential limitation of modeling
cultural selection as a function of vaccination frequency is that the potential values of the cul-
tural selection coefficient could be restricted when vaccines are scarce. The shape of our default
cultural selection coefficient function (S1 Fig) assumes less variability in the perceived benefit
of vaccination at low levels of vaccination coverage. Since the major limiting factor of vaccina-
tion frequency in a vaccine-scarce environment could be vaccine availability, rather than vacci-
nation behavior, the higher limit of population vaccination frequency is externally reduced
based on vaccine supply, thus biasing vaccine perception and vaccination selection in our
model to be close to σ
max
(highest selection for vaccination). It is possible that the trajectory of
cultural selection for vaccination may change when vaccines are scarce: perhaps patterns of
perceptions change with the knowledge of vaccine (un)availability [51], thus potentially pro-
viding an avenue for further exploration with this model. Though not explicitly discussed, we
test scenarios in which the selection coefficient is more sensitive to changes in lower vaccina-
tion frequencies, which might be relevant when vaccines are inaccessible (S3 Fig,column
5–6). Compared to our baseline selection function (S3 Fig,column 3), the change in sensitivity
does give rise to slightly lower levels of vaccination coverage at equilibrium when confidence
transmission by mixed-trait couples is higher.
In addition, our model simplifies the process of human population turnover with discrete
generations; in reality, of course, population turnover is asynchronous and multiple genera-
tions can have cultural interactions with one another [9]. However, this simple model is able
to demonstrate interesting scenarios that confirm the importance of understanding the culture
of the communities in which public health policies act, and how the cultural landscape might
affect specific outcomes. A community is most protected from VPD outbreaks if two condi-
tions are met: vaccination coverage achieves or exceeds herd immunity levels, and future vacci-
nations are not threatened by underlying vaccine hesitancy. The effects that we observe as a
result of varying the cultural selection function suggest that an “unwavering” (positive) percep-
tion of vaccination is better for maintaining higher levels of vaccination coverage than one
that varies with vaccination coverage. This highlights a significant issue in increasing vaccina-
tion in the absence of (severe) disease as perceptions are shaped by experience of both the dis-
ease and measures used to address the disease. Since increasing vaccination coverage might
require different strategies than increasing confidence, we encourage public health policy-
makers to consider both beliefs and behavior patterns in their outreach efforts and informa-
tion campaigns.
The results of our simulations are congruent to those observed in other behavior change
model studies [16]. For example, Epstein et al. [17] demonstrated using a “triple contagion”
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Modeling the interactions between vaccine hesitancy, accessibility, and mandates
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model, in which a disease, fear of a disease, and fear of a vaccine can each be transmitted
between individuals, that high vaccination coverage may be achieved when fear of a vaccine is
low and fear of the disease is high. Though our model uses different methods of transmission,
we arrive at similar conclusions; for example, our model predicts higher vaccination coverage
when the cultural selection coefficient is high, suggesting a higher perceived value of vaccina-
tion (and thus lower fear of the vaccine). Similarly, faster spread of vaccine fear in the Epstein
et al. study could be interpreted similarly to higher probabilities of transmitting vaccine hesi-
tancy (lower C
1
=C
2
values) in our model, and we also observe reduced vaccination coverage
in these scenarios.
Another external factor that can affect these dynamics, but has not been explored in this
study, is the occurrence of a pandemic and the introduction of a novel vaccine. The COVID-
19 pandemic appears to have had complex ramifications on attitudes toward other vaccines.
For example, a global survey assessing caregiver willingness to vaccinate their children against
influenza showed that changes in caregiver risk perception due to COVID-19 and concerns
that their children may have contracted COVID-19 resulted in a significant upward shift in
caregiver’s plan to vaccinate against influenza following the pandemic–approximately 29% of
caregivers who had not vaccinated their children in the previous season (2019–2020) planned
to vaccinate in the next [52]. A recent report on kindergarten vaccination rates in Tennessee
illustrated a temporal correlation between the pandemic and an increase in the use of non-
medical, particularly religious, vaccine exemptions [53]. The same report also noted that the
barriers to obtaining routine medical care and administrative challenges in schools during the
COVID-19 pandemic contributed to increased vaccine-hesitant behavior such as modifying
vaccine schedules.
Additionally, an experimental study of the effects of COVID-19 vaccine scarcity [54] found
that vaccine scarcity could decrease the willingness to vaccinate, but it did not, however, affect
the perception of risk or protection associated with the vaccine. Though the perceived risk in
our model is modulated according to vaccination frequency (that is, in our model, perceptions
are modulated by vaccination coverage), our simulations reveal an intuitively similar pattern:
vaccination is reduced overall when vaccines are scarce. However, while perception may be
modulated in our model, we do observe an increase in vaccine confidence under conditions
that result in low vaccination coverage. This is in line with the findings of Pereira et al. [54] as
vaccine-confident individuals may choose to forgo vaccinations for the benefit of others if
resources are limited, such as when the COVID-19 vaccine was relatively inaccessible when it
was initially released, while still maintaining (and transmitting) their vaccine beliefs. In con-
trast to our model, which focuses on established childhood vaccines, the Pereira et al. study
focused on adult vaccination with the novel COVID-19 vaccine. The differences between the
vaccine target populations (e.g. child vs. adult) and the interacting individual values (e.g. com-
passion for higher-risk individuals in foregoing one’s own vaccinations when vaccines are
scarce) may produce differing dynamics requiring different public health approaches.
In sum, our model shows, in both mandate and inaccessibility scenarios, that the probabil-
ity of transmitting vaccine-positive attitudes is a strong predictor of whether future vaccination
coverage is high or low (Figs 2,5and 6). We also demonstrate that vaccine efficacy and per-
ceived value are important to maintaining sufficient levels of vaccination coverage, especially if
vaccine confidence is not being robustly transmitted (or maintained in adulthood), regardless
of vaccination scenario (Figs 2,5and 6). Thus, our model demonstrates the importance of
clear and accurate communication about vaccines even when vaccination is mandatory and
resulting coverage is high, to reduce the spread of inaccurate information that can foster vac-
cine hesitancy and hinder the uptake of future vaccines. Taken together, the results our model
suggest that combatting low or declining vaccine uptake would take a sophisticated approach
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Modeling the interactions between vaccine hesitancy, accessibility, and mandates
PLOS Global Public Health | https://doi.org/10.1371/journal.pgph.0001186 October 4, 2023 14 / 19
that targets the physical vaccination behavior (availability and mandates) while simultaneously
addressing a population’s constantly evolving vaccine perceptions.
Supporting information
S1 Text. Detailed Methods describing model construction and parameter nomenclature.
(PDF)
S2 Text. Recursion equations for model of vaccine niche construction.
(PDF)
S1 Fig. Cultural selection coefficient function. The cultural selection coefficient considers
both health and non-health related effects, and the function was constructed by fitting a curve
to specified conditions. The selection coefficient (σ; vertical-axis) is dependent on the fre-
quency of vaccinated individuals (V
+
) in the population (horizontal-axis). σ
max
is the maxi-
mum cultural selection coefficient associated with being vaccinated. Perceived vaccine benefit
is reduced as vaccination coverage increases, since the negative effects of the disease will be
less apparent.
(PDF)
S2 Fig. Attitude transition probability function. Attitude transition probability functions
were constructed by fitting a curve to specified values. Attitude transition probability (vertical
axis) is a function of the vaccination frequency in the population (V
+
; horizontal axis). The
probability that a vaccine hesitant individual adopts vaccine confidence (A
−
to A
+
transition
probability, shown in dashed black) is determined by the function A!Confident, and the
probability that a vaccine confident individual adopts vaccine hesitancy (A
+
to A
−
transition
probability, shown with a solid blue line) is determined by the function A!Hesitant.
(PDF)
S3 Fig. Selection trajectories affect outcomes at equilibrium when vaccines are accessible.
Heatmaps showing equilibrium vaccine coverage and vaccine confidence levels with an acces-
sible vaccine and no mandate (Section B), with an accessible vaccine and a less strict mandate
(Section C) and an environment with vaccines somewhat inaccessible (Section D), employing
various cultural selection (σ) functions: (A1)σdoes not depend on vaccination coverage, (A2)
σdecreases after a high herd-immunity threshold of ~90% coverage, (A3)σdecreases after a
medium herd-immunity threshold of ~70% coverage (baseline function), (A4)σdecreases
after a low herd-immunity threshold of ~50% coverage, (A5)σdecreases linearly as vaccina-
tion coverage increases, (A6)σdecreases according to a cubic function. We vary C
1
=C
2
(con-
fidence transmission probability of mixed-attitude couples) on the vertical axis, and maximum
selection coefficient σ
max
(indicative of the perceived value of vaccinating offspring) on the
horizontal axis. Unspecified parameters are given in Table 1 with σ
max
held at 0.1 for all func-
tions shown in Section A but varied in the heatmaps in Sections B-D. Black and white dashed
lines indicate the area of the heat maps in which vaccination and confidence frequencies equil-
ibrate between 0.1 and 0.9.
(PDF)
S1 Table. Presence (+) and absence (–) subscript assignments. Demonstrating the trait pres-
ence (+) and absence (–) combinations associated with m, n subscripts. For example, the + ×–
combinations is associated with m and n subscript value 2: an A
+
×A
−
pairing transmits A
+
at
probability C
2
. This rule applies to parameters C
n
,b
m
,B
m,n
,c
n
, as shown in S2 Table.
(PDF)
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Modeling the interactions between vaccine hesitancy, accessibility, and mandates
PLOS Global Public Health | https://doi.org/10.1371/journal.pgph.0001186 October 4, 2023 15 / 19
S2 Table. Probabilities of trait transmission to offspring from cultural trait pairings. For
each mating, we give the probability of transmitting each trait, and corresponding influence
parameters. The probability of vaccinating an offspring, B
m,n
, depends on both the parents’
vaccination state (V
+
: vaccinated; V
−
: unvaccinated) and their attitude state (A
+
: vaccine confi-
dent; A
−
: vaccine hesitant). B
m,n
is informed by the influence of parents’ vaccination states (V)
on their decision to vaccinate (b
m
) and by the influence of their vaccine attitudes (A) on their
decision to vaccinate (c
n
). For each parental pairing, the probability of not vaccinating an off-
spring is 1 –B
m,n
. Each pairing transmits confidence in vaccines at a rate C
n
, and hesitancy at
rate 1 –C
n
. The parameters b
m
,c
n
, and C
n
are set as constants for each simulation, and B
m,n
is
calculated from these.
(PDF)
S3 Table. Probability range shift assignments. Each probability was grouped according to
baseline vaccination probability calculations. All probabilities in a group hold the value
assigned to that group in the range, as shown. C
n
probabilities were assigned values as shown,
with C
0
taking the lowest value in the range and C
3
taking the highest. The lowest probability
range group is given as an example of value assignment.
(PDF)
S4 Table. Quantitative differences between equilibrium frequencies with low transmission
of vaccine confidence. The mean and median of vaccination coverage and vaccine confidence
levels at equilibrium were calculated for the section of the heatmaps in Fig 2 for which C
1
=C
2
<0.5 (blue in vaccination coverage heatmaps; red in the confidence level heatmaps).
(PDF)
Author Contributions
Conceptualization: Kerri-Ann M. Anderson, Nicole Creanza.
Data curation: Kerri-Ann M. Anderson.
Formal analysis: Kerri-Ann M. Anderson, Nicole Creanza.
Funding acquisition: Kerri-Ann M. Anderson, Nicole Creanza.
Investigation: Kerri-Ann M. Anderson.
Methodology: Kerri-Ann M. Anderson.
Project administration: Nicole Creanza.
Software: Kerri-Ann M. Anderson, Nicole Creanza.
Validation: Kerri-Ann M. Anderson.
Visualization: Kerri-Ann M. Anderson, Nicole Creanza.
Writing – original draft: Kerri-Ann M. Anderson, Nicole Creanza.
Writing – review & editing: Kerri-Ann M. Anderson, Nicole Creanza.
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