Background
As we enter the unfamiliar territory of the worst global pandemic in a century, the worldwide emergence of noncompliance with public health measures aimed at limiting the spread of SARS-CoV-2 is not as surprising as it may seem at first blush [
1,
2]. During the 1918 Influenza pandemic, for example, resistance to public health measures aimed at reducing the spread of disease manifested at the individual level, leading to violence [
3] and stiff punishments for “mask slackers” [
4,
5]. Anti-mask protesters led large demonstrations [
6], and city councils questioned the value of mask ordinances [
7,
8] with emotionally charged language: “under no circumstances will I be muzzled like a hydrophobic dog” [
9]. The phrasing may be dated, but the sentiment echoes precisely across a century [
10].
For COVID-19, a number of features of the disease facilitate noncompliance with disease control measures such as masking and vaccination. Hospitalization and death happen away from the public eye, and our changing understanding of the mechanism of transmission, the risk of mortality and the long-term consequences of the disease have favored the spread of misinformation. The spread of confusion and misinformation has been a common feature for other novel pathogen-induced pandemics such as Ebola [
1,
11,
12] and the 1918 Flu [
13]. While the existence of pandemic denialism was easy to anticipate [
14], the unique characteristics of COVID-19 amplify its effect. Studies suggest that asymptomatic or presymptomatic patients account for up to 40% of SARS-CoV-2 transmission [
15], severely limiting the utility of more traditional and intuitive disease control measures such as symptomatic isolation [
16]. The high reproductive number (R
0) of SARS-CoV-2 (the average number of individuals who contract a contagious disease from one infected individual, which was reported to be 5.7 in the early days of the pandemic in Wuhan [
17]) creates the potential for explosive growth in situations where the virus has not been completely eradicated, as has been demonstrated by a massive second wave in many European countries [
18,
19]. Making matters worse, estimates for natural immunity as a consequence of SARS-CoV-2 infection range from 6 to 24 months [
20‐
22], creating the potential for multiple waves of disease in the short term.
Thus, the unique characteristics of COVID-19 raise the possibility that noncompliance with public health measures may create conditions that make disease control in the short term impossible or prevent any return to pre-pandemic lifestyles in the long run. With this in mind, we asked three questions: First, in the specific case of COVID-19, are there circumstances that lead to a perceived benefit to noncompliance with public health measures for a substantial portion of the population? Second, what is the impact of noncompliance on the attainability of suppression of SARS-CoV-2 spread? Third, what is the magnitude of the negative externality (a cost incurred by them that is not of their choosing) created for the compliant population as a result of noncompliance of others?
We approached the first question from the perspective of game theory, which has previously been applied to decision-making around vaccine uptake [
23]. Our approach involved building a mathematical model of the strategic interaction between compliers and non-compliers for a given (nonpharmaceutical or biomedical) intervention aimed at controlling SARS-CoV-2 spread. The approach weighs the perceived cost of complying with an intervention against the perceived benefit to determine under what conditions individuals acting in their own self-interest will choose to comply. A number of studies have previously examined noncompliance with measures to control SARS-CoV-2 spread through a social-sciences lens, exploring social and psychological risk factors associated with this behavior. These studies, from a range of different countries, have linked noncompliance to Dark Triad traits (i.e., Machiavellianism, Psychopathy Factor 1, and narcissistic rivalry [
24]), antisocial behaviors [
25], higher levels of impulsivity [
26] and a prior record of delinquent behaviors [
27]. A positive, rather than normative, framing of the question involves exploring the set of conditions for which the perceived benefit of noncompliance to the individual is simply greater than the perceived benefit of compliance. This allows us to examine the problem of compliance from the limited perspective of individuals optimizing for their own benefit without accounting for the common good, particularly relevant in the context of arguments based on personal liberty being used as a justification for noncompliance [
28].
For the next two questions, we used a Susceptible-Exposed-Infected-Recovered-Susceptible (SEIRS) epidemiological modeling framework with a duration of immunity ranging from 6 to 24 months to explore the range of levels of compliance and intervention efficacy required for disease suppression. Our intent in this study was to explore a possible link between the free optimization of individuals’ outcomes as a result of noncompliance, the externalities generated by those choices, and the implications for epidemic control in the short and long term.
Methods
Game theory modeling of compliance with interventions aimed at limiting SARS-CoV-2 spread
For the purposes of this work, we defined an “intervention” as being a public health measure that reduces the transmission of SARS-CoV-2. This may be a nonpharmaceutical intervention, such as masks, or a biomedical intervention, such as a vaccine. Compliance with an intervention is defined as a binary choice. An individual can choose whether or not to comply with an intervention based on the perceived costs and benefits of the intervention. We modeled this choice using a game theoretic framework, which compares the perceived cost of compliance (reduction of quality of life resulting from the intervention) in relation to perceived cost of infection (risk-weighted morbidity/mortality burden) to the individual. Individuals derive a benefit or cost (i.e., a payoff) from interactions with other individuals in the population, who can also either be compliers or noncompliers.
We sought to determine the conditions under which noncompliance is the Nash equilibrium, or optimal behavior strategy for individuals seeking to maximize their own payoff. In a Nash equilibrium, the expected payoff to noncompliers is higher than the payoff to compliers when interacting with any other individual in the population [
29].
For this two-strategy “game”, the payoffs to compliers and noncompliers are given in Table
1, where
q is the cost of the intervention,
αi is the fraction of infected individuals of type
i, and
mi is the perceived cost of infection for type
i individuals, where
i can either be
u (noncompliers) or
v (compliers). The cost
mi is the perceived risk of a negative health outcome given exposure to an infected individual. Other parameter definitions are given in Table
2. As in the SEIRS model, the efficacy of the intervention in protecting the individual from getting infected (
b) is assumed equal to the efficacy in preventing transmission (
c) (i.e.
b =
c).
Table 1
Payoff matrix for compliers/noncompliers
Noncomplier payoff | -αumu | -αvmuc |
Complier payoff | -q - αumvb | -q - αvmvbc |
Table 2
Model parameters for SEIRS model
Latency period | 1/ α | 3 days | |
Reproductive number | R0 | 5.7 individuals | |
Infectious period | 1/ γ | 10 days | |
Natural immunity duration | 1/ δ | 18 months | |
Infection fatality rate | σ | 0.68% | |
Population birth rate | μ | 1% annually | |
Population death rate | λ | 0.9% annually | |
Fraction compliant | f | Variable | |
Protective efficacy | 1-b | Variable | |
Transmission reduction | 1-c | Variable | |
Noncompliance is a Nash equilibrium if and only if both of the following conditions are met:
$$ -{\alpha}_u{m}_u>-q-{\alpha}_u{m}_vb $$
$$ -{\alpha}_v{m}_uc>-q-{\alpha}_v{m}_vb. $$
Or, equivalently
$$ {\alpha}_u<\frac{q}{\left({m}_u-{m}_vb\right)} $$
$$ {c\alpha}_v<\frac{q}{\left({m}_u-{m}_vb\right)}. $$
Since noncompliers are much more likely to be infected than compliers, αu > cαv. Therefore, meeting the first condition alone (noncompliers receive a greater payoff than compliers when interacting with other noncompliers) is sufficient for noncompliance to be a Nash equilibrium.
SEIRS model of SARS-CoV-2 spread
To support predictions of short- and long-term outcomes for the COVID-19 pandemic, we built an SEIRS ordinary differential equations (ODE) model to account for disease spread, waning immunity in the recovered population, and the acceptance of a vaccine or non-pharmaceutical intervention (NPI) in a fraction of the population. The model consists of two parallel sets of SEIR compartments representing the vaccinated or NPI-compliant (“compliant”) and unvaccinated or NPI-noncompliant (“noncompliant”) populations. The compliant population has a reduced risk of infection which is conferred by the vaccine or NPI (“protective efficacy”). The compliant population may also have a reduced risk of transmission to others upon infection resulting from physiological or behavioral changes (“transmission reduction.”) All compartments were assumed to be well-mixed, meaning that compliant and noncompliant individuals are in contact within and between groups. Vaccination or NPI compliance-based reductions in susceptibility, transmissibility, or contact rate were assumed to be time-invariant, reflecting the most optimistic case for disease control. Similarly, individuals do not move between the compliant and noncompliant compartments. Model equations are summarized below:
$$ \frac{d{S}_v}{dt}=-\upbeta {bS}_v\left(c{I}_v+{I}_u\right)+\updelta {R}_v+ f\mu -\lambda {S}_v $$
$$ \frac{d{E}_v}{dt}=-\upalpha {E}_v+\upbeta {bS}_v\left(c{I}_v+{I}_u\right)-\lambda {E}_v $$
$$ \frac{d{I}_v}{dt}=-\upgamma {I}_v+\upalpha {E}_v-\lambda {I}_v $$
$$ \frac{d{R}_v}{dt}=\upgamma {I}_v\left(1-\sigma \right)-\updelta {R}_v-\lambda {R}_v $$
$$ \frac{d{S}_u}{dt}=-\upbeta {S}_u\left(c{I}_v+{I}_u\right)+\updelta {R}_u+\left(1-f\right)\mu -\lambda {S}_u $$
$$ \frac{d{E}_u}{dt}=-\upalpha {E}_u+\upbeta {S}_u\left(c{I}_v+{I}_u\right)-\lambda {E}_u $$
$$ \frac{d{I}_u}{dt}=-\upgamma {I}_u+\upalpha {E}_u-\lambda {I}_u $$
$$ \frac{d{R}_u}{dt}=\upgamma {I}_u\left(1-\sigma \right)-\updelta {R}_u-\lambda {R}_u $$
Where S represents the susceptible population, E the exposed population, I the infectious population, and R the recovered population. Subscript v represents the vaccinated or compliant sub-population, while subscript u represents the unvaccinated or noncompliant sub-population. Model parameters are summarized in Table
2.
According to the CDC, the R
0 for SARS-CoV-2 under pre-pandemic social and economic conditions is estimated to be approximately 5.7 [
17]. For the purpose of this study, an R
0 of 5.7 is used to represent epidemiological conditions under a theoretical full return to pre-pandemic activity. The contact rate
β is derived from the relationship between R
0 and the infectious period:
$$ \beta =\gamma {R}_0 $$
In this “normal” scenario, disease reduction interventions reduce the compliant population’s infection rate by the factor b, which represents the intervention’s protective efficacy, and the compliant population’s transmission rate by the factor c, representing the intervention’s reduction in transmissibility. For simplicity, the reduction of transmission was assumed to be equivalent to the protective efficacy (reduction of susceptibility) of each intervention. This is an optimistic assumption; in some cases, an intervention may provide little or no reduction in transmission in compliant infected individuals.
The model’s initial conditions are set to approximate current United States disease prevalence and seroprevalence (as of September 2020) [
36]:
$$ I\left(t=0\right)=0.2\% $$
$$ R\left(t=0\right)=8\% $$
Our model lacks a seasonal component for SARS-CoV-2 transmission, as such associations have been conjectured [
37] but not proven, and it also assumes a 18-month duration of natural immunity, as an optimistic estimate based on the duration of antibody responses currently reported [
20‐
22]. The disease-preventing interventions and return to normalcy (which would correspond to a return to the pre-pandemic R
0 of 5.7) are assumed to occur at the beginning of the simulation interval.
Compliance sweeps
To gauge the impact of NPI or vaccine compliance on population outcomes, we varied the compliant fraction under a series of simulated vaccine or NPI deployment schemes with varying degrees of protective efficacy. The model allows tracking of outcomes for the population as a whole and for the compliant and noncompliant sub-populations.
Discussion
Our work supports the case that noncompliance is embedded in human nature, as individuals optimizing their own self-interest can justify their actions in terms of their own perceived cost-benefit.
Individuals may perceive noncompliance as favorable for a number of reasons [
38,
39]. They may view their own risk of being infected as lower than average (the optimism bias [
40], which has been documented as a risk factor in predicting noncompliance for SARS-CoV-2 spread mitigation measures [
41]), or they may view their own risk of adverse outcomes as a result of infection as being lower than average [
27]. Globally, the public health messaging around noncompliance has focused on the low risk of death for younger individuals [
42‐
44] and has invoked the imagery of “shielding” highly vulnerable populations from the disease [
45] as an altruistic motive [
46]. To the extent that many countries in the Americas and Western Europe at present are facing uncontrolled disease spread, it is likely that invoking altruism may not be the most effective means of disease control. Underestimating the risk of infection may also lead to individuals believing that noncompliance is the better choice.
The interplay between risk perception and compliance is complex, and fear may also play a paradoxical role in noncompliance. A number of studies have demonstrated a link between emotions and cognitive assessment of risk. In particular, high levels of fear coupled with a low sense of efficacy may create a defensive response in individuals who then proceed to dismiss the risk (“we’re all going to die anyway”) [
47]. Studies have also shown that psychological affect plays a role in risk perception in individuals who are less comfortable and/or experienced interpreting probability [
48,
49].
Regardless of the underlying causes, a Nash equilibrium of noncompliance creates a Tragedy of the Commons situation, where individuals acting according to their own self-interest create outcomes that are suboptimal for the common good by spoiling the shared resource through their collective actions. The term Tragedy of the Commons dates back to an influential article written over 50 years ago [
50], which in turn was inspired by a nineteenth-century essay describing grazing practices of farmers. Tragedy of the Commons situations are indeed common in the fields of economics, politics, environmental policy and sociology. What makes Tragedy of the Commons situations particularly intractable is that it usually only takes a small proportion of individuals optimizing for their own self-interest to create devastating externalities for the rest of the population. This behavior underscores the limitations of the laissez-faire, individualistic approach to disease control during a pandemic. A laissez-faire approach is often said to lead to the best outcomes for the population overall as part of utilitarian economic theory [
51], as put forward by John Stuart Mill. However such an approach actually violates the standard originally laid out by Mill by which a person’s liberty may be restricted: “The only purpose for which power can rightfully be exercised over any member of a civilized community, against his will, is to prevent harm to others” [
52].
Given the ubiquity of the problem, some public policy solutions can be found that have close analogies to successful interventions in other spheres of human activity. First, public health messaging that seeks to alter the Nash equilibrium at an individual level are worth exploring. In individualistic societies, this may be accomplished by de-emphasizing altruism and focusing on the individual cost-benefit. One way this may be achieved is by emphasizing the long-term morbidity costs (such as cryptic heart, lung, brain and kidney damage) as have been documented to occur in even asymptomatic COVID-19 patients in an age-independent manner [
53‐
55]. An additional approach is to provide an accurate and current picture of the risk of contracting the disease. Second, public health policy that creates costs for noncompliers may serve to shift some of the externalities back on to the originator (as was the case with mask ordinances during the 1918 Flu [
4] and fines imposed for noncompliance with measures aimed at limiting SARS-CoV-2 spread in some countries [
56,
57]). Third, public health interventions should engage at the level of the community. Public health and communications experts could test a number of different messages that underscore the downside of negative externality-creating behavior at a societal level. Some of these approaches have been used previously in the context of vaccine acceptance [
58]. It is worth noting that our analysis points out a potential mechanism for the high levels of compliance observed in countries such as South Korea [
23], with strong societal norms and a positive view of restrictions aimed at limiting SARS-CoV-2 spread such as mask-wearing [
59,
60]. In these cultures, the prevailing cultural beliefs may serve to lower the cost of the intervention. In this context, we note that there is a modest association (Fig.
S4, see
Supplementary Figures) between societies with strong societal norms (“tight cultures” [
61]) and the total case count per million at this point in the pandemic (
p = 0.04).
From the perspective of biomedical interventions, our work points out that interventions with a high degree of protective efficacy are required for complete suppression of SARS-CoV-2, making this disease particularly challenging to control. Highly effective interventions have the dual effect of making the creation of negative externalities less beneficial for the noncompliant population (Fig.
4), and also increasing the benefit to the compliant population (Fig.
6). Notably, highly effective interventions provide more wiggle room for public policy, as the threshold level of compliance required for the complete suppression of SARS-CoV-2 spread drops from approximately 95% for a minimally effective intervention to approximately 80% for highly effective interventions. Another path to disease suppression lies in implementing passive interventions that reduce the R
0, such as improving ventilation. Such passive interventions, not being subject to the problem of individual noncompliance, can serve to lower the bar for compliance for any given intervention to achieve complete suppression (Fig.
S2, see
Supplementary Figures).
Our work has a number of key limitations. First, we assume that the impact of biomedical and nonpharmaceutical interventions is not variable over time. In practice, changes in SARS-CoV-2’s transmissibility or response to interventions, such as seasonal fluctuations and genewration of new viral variants, will affect the long-term trajectory of the pandemic and are not accounted for in our model. Additionally, many factors may cause individuals to change their compliance behavior over time, which we also did not incorporate into our model. For example, in some settings, “pandemic fatigue” may drive increased noncompliance with nonpharmaceutical interventions over time [
62], and relaxations of individual caution and public health guidelines may follow improvements in regional transmission, creating reactive variability in intervention effectiveness. Although biomedical interventions such as vaccines are less susceptible to variability in day-to-day decision-making, immunity to SARS-CoV-2 is expected to wane over a period of months [
20‐
22], which can be expected to impact the duration of vaccine protection. Challenges in vaccine distribution and compliance may compound this waning immunity, reducing the apparent effectiveness of vaccines at the individual and population scale. Additionally, we assumed that compliant individuals have a reduced risk of transmission upon infection, equal to their reduction in risk of infection. This indirect benefit is challenging to measure in clinical trials, and preclinical studies show that some vaccine candidates are capable of reducing nasal viral load (and by implication, risk of transmission) in vaccinated animals [
63,
64], while others are not [
65,
66]. As additional data becomes available on evolution of SARS-CoV-2 and on the efficacy of interventions aimed at preventing SARS-CoV-2 spread, further studies on the impact of intervention noncompliance could provide more accurate predictions.
Taken together, our work demonstrates that noncompliance with measures to control SARS-CoV-2 spread is at once easy to justify on an individual level and leads to devastating public health consequences. Even under optimistic assumptions about the transmission benefit and durability of preventive interventions, noncompliance presents a significant obstacle to SARS-CoV-2 suppression. Three key messages are worth keeping in mind. First, the importance of focusing on complete suppression as a desirable end goal for SARS-CoV-2 (Fig.
5) and as a prerequisite for a return to a pre-pandemic lifestyle. SARS-CoV-2 is highly transmissible and can be expected to circulate at high rates if it becomes endemic. Second, the need for public policy to focus on compliance as a key prerequisite for both short-term suppression (Fig.
3) and long-term complete suppression (Fig.
5) of SARS-CoV-2 spread, and to seek ways to alter the space where compliance is the Nash equilibrium by increasing the cost of noncompliance. Finally, the need to focus on highly effective interventions from a biomedical perspective and to view partially effective prophylactics as contributors to the solution rather than the solution in its entirety.
It is our hope that this work draws the attention of the biomedical community to how high the bar is actually set for us to return to normalcy, and to public policymakers to highlight the need for concerted action that is focused on complete suppression of SARS-CoV-2 spread.
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