key: cord-1010946-15spu6j5 authors: Carrignon, S.; Bentley, R. A.; Silk, M.; Fefferman, N. H. title: The 'Icarus effect' of preventative health behaviors date: 2020-06-09 journal: nan DOI: 10.1101/2020.06.08.20126029 sha: b09e764951f8462143f319b67a15045e92f858c5 doc_id: 1010946 cord_uid: 15spu6j5 Ongoing efforts to combat the global pandemic of COVID-19 via public health policy have revealed the critical importance of understanding how individuals understand and react to infection risks. We here present a model to explore how both individual observation and social learning are likely to shape behavioral, and therefore epidemiological, dynamics over time. Efforts to delay and reduce infections can compromise their own success, especially in populations with age-structure in both disease risk and social learning - two critical features of the current COVID-19 crisis. Our results concur with anecdotal observations of age-based differences in reactions to public health recommendations. We show how shifting reliance on types of learning affect the course of an outbreak, and could therefore factor into policy-based interventions. the longer term. 48 Here we frame the impact of the 'Icarus paradox' as dependent on infor-49 mation and timing. At what point do individuals observe enough infections 50 around them to adopt preventative behavior as their own cost/benefit decision? 51 Before this point, in the absence of government directives, social norms may be 52 needed to encourage protective behaviors as people are not yet observing many 53 infections. We expect that early in an outbreak, the link between protective 54 behaviors and being uninfected will not yet be transparent. As infection preva-55 lence increases, and the benefits become more obvious to individuals, social 56 learning becomes less necessary to facilitate preventative behaviors. 57 To explore these complex behavioral and disease dynamics, we employ an 58 agent-based modelling approach. 59 Here we take the approach of discrete behavioral choice with social influence 61 [12, 13, 14, 15] , where we model decisions as based on a separable combina-62 tion of two components: observational and social learning. Importantly, the 63 underlying physical contact network through which a disease might spread [16, 3 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 9, 2020. . https://doi.org/10.1101/2020.06.08.20126029 doi: medRxiv preprint beliefs about their health risks [22, 23, 10, 20] . For example, the perceived utility 72 of social distancing likely increases as more illnesses and deaths are observed. 73 In typical formulations of discrete choice theory or quantal response theory, 74 the probability that an agent chooses choice i at time t is proportional to e κUi(t) + 75 i (t), where κ is the transparency of choice and U i (t) is the intrinsic utility of the 76 choice, and i (t) is a noise term [24, 12, 13, 25] . Normalized across all choices, 77 the shape of the probability function has a sigmoid shape with respect to the 78 utility of the choice. In our model, we therefore assume the probability of choice through ob-80 servational learning takes on a sigmoid form, shaped by two parameters. One 81 parameter for this is the point at which one option has a higher utility than 82 the other, U i > U j : we call this the 'inflection point', ν. In our model, this how a group's average behaviour influences its individuals [26, 27] . 89 The second parameter for the observational learning component is trans- One way of effecting behavioral change is when an individual learns by them-97 selves, by looking at the health status of people of the same age and estimating 98 if they should switch to the other behavior. Given I a , the proportion of infected 99 individuals in the same age cohort, a, the probability for an individual i to 100 switch from 'non-adherent' status, N A, to 'adherent' status, N A, is defined as: where κ represents the transparency of choice-determining the steepness of the 102 sigmoid curves-and ν defines the point at which the individual has a 50% prob-103 ability to switch to adherent status, A. The influence of ν and κ, respectively, 104 on the probability of adoption, P , is illustrated in Figure 2 . The same function is used to calculate the probability for an individual to 106 switch back from adherent to non-adherent behavior given the fraction of people 107 in the age cohort who are not infected, (1 − I a ): where ν r is inflection point for reverting to N A behavior (and can be different CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 9, 2020. contagions that impact health outcomes," [20] . To simplify their complex role 113 for our model, we employ the useful distinction between complex beliefs versus 114 'simple' social contagions [20] . Here we treat social distancing and related pro- selecting option i is proportional to its current frequency or popularity, p i,t [12, 123 13, 26] . 124 We also assume that social learning of simple behaviors (as opposed to com-125 plex skills learned over years) is age-restricted, in that people will only copy 126 others in their own age cohort. For convenience, this assumption conflates two 127 observations, that: (a) age cohorts tend already to share similar beliefs and 128 preferences, derived from both ontogeny and broadly shared socio-economic 129 landscape during early years of development [28, 29, 30, 31, 32, 33, 34] , and (b) 130 conformity tends to be age-dependent with age-biased social learning [35] . The ABM consists of agents who are involved in two inter-related processes, 137 the contagion of a disease in SIR fashion [36] , and the spread of protective 138 5 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 9, 2020. . Simulations were run with the parameters described in the Table 1 with The parameters were selected such that, overall, agents encounter a mean of 12 155 individuals per 24 time steps, such that each time step represents one hour. The 156 recovery times in the SIR model were thus calculated to represent 8 to 14 days 157 as a reasonable approximation for COVID-19 [37] . To explore the impact of learning on the disease outcomes over the course of 159 an outbreak, we ran three sets of models. We first ran two baseline conditions 160 in which individual behavior is held constant as either non-adherent (worst case 161 scenario) or adherent (best case scenario) over the course of the simulation. We 162 subsequently ran the models with the parameters described in Table 1 is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 9, 2020. . https://doi.org/10.1101/2020.06.08.20126029 doi: medRxiv preprint min(I max ), respectively, as well as the longest and shortest times to reach the max, as max(τ ) and min(τ ), respectively. Since these dimensions will tend to 172 be inversely correlated, we defined a metric, δ(s), for a set of simulations s 173 summarizing both: is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 9, 2020. . https://doi.org/10.1101/2020.06.08.20126029 doi: medRxiv preprint is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 9, 2020. It is not surprising that such risk-averse behaviors would protect a population. The challenge is that the risk needs to observable. Hence protective behaviors 232 may be not be adopted until infection rates are very high, especially if most 233 symptomatically infected individuals are not be publicly visible (e.g., remaining 234 at home or in hospital). For this reason, low transparency of choice-such as poor or conflicting in-236 formation -can 'jump-start' adoption of protective behaviors by stretching out 237 the inflection into a range, such that some individuals 'mis-estimate' infection 238 risks as enough to trigger their decision (see Fig. 5 ). However, this result re-239 lies on the breadth of the distribution of responses to low transparency, rather 240 than an alternative case in which either leadership or social norms cause low 241 transparency to lead to greater average hesitancy to take any action [42] . Social learning dynamics were also crucial to outcomes. In social learning 243 9 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 9, 2020. . Parameters to switch from Adherent to Non-Adherent Worst Best Figure 5 : Joint posterior distributions for the parameters used to switch from Non-Adherent to Adherent (left column) and for the parameters used to switch back from Adherent to Non-Adherent (right column). The 2d areas represent the 70% and 90% HDR (High Density Region) ie, the smallest areas within which respectively 70% and 90% of the parameters combination fall (for the mathematical definition of HDR and how they can be represented see [38] . Lighter colors represent the 90% HDR whereas darker represent the 70% HDR. The top row represent the value for those parameters that minimize (in blue) or maximize (in red) the number of infected people at time step 150. The bottom row shows the parameters that minimize (in blue) or maximize (in red) δ (as defined in Equation 1) at the end of the simulation (1500 time steps). The marginal posteriors for each parameter taken separately are drawn in the margin. . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 9, 2020. . theory, "copying recent success" is often the best strategy [43] . If the disease symptoms/prevalence are transparent, copying healthy individuals ('success') 245 should increase protective behaviors as disease prevalence increases. Because 246 COVID-19 can be asymptomatic, however, transparency in this respect may be 247 low. Infected individuals may seem healthy, such that non-protective behaviors 248 can be copied even through a "copy success" strategy. This lack of transparency 249 may critically compromise our ability to rely on learning-only strategies for 250 successful disease risk containment. These effects may be heightened among young people, for whom infection is more frequently asymptomatic and who are also socially influenced 253 by peers of similar age [35] . Hence, while lower fatality risk from COVID-19 may In our models, we have also assumed that choices are rational and focused 281 only on epidemiological risk. In reality, social distancing involves considerable 282 social and economic costs [45] ). Human decision-making is also never fully ra-283 tional, especially during period of stress [46] . Further, we have here explored 284 only one potential route of social learning, in which individuals simply copy 285 the behaviors of perceived healthy individuals. More nuanced approaches may 286 emphasize preferentially copying people who share your beliefs, alignment with 287 deeply-held beliefs or values, and other social learning strategies [47, 48, 49, 288 20] . Similarly, we have construed frequency of contact within a spatial radius 289 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 9, 2020. . https://doi.org/10.1101/2020.06.08.20126029 doi: medRxiv preprint to be the only medium for social derivation of learning. In reality, of course, however complicated or accurate [20, 50, 51, 52, 20] . This raises many interest- These considerations may be critical in shaping policies that will foster pub-304 lic adherence. True leadership must sometimes accept the burden of enacting 305 policies doomed to be unpopular. However, understanding of the role of the 306 'Icarus paradox' in public health safety may help preemptive design of policies 307 that anticipate increasing non-adherence as they are increasingly effective. . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 9, 2020. . https://doi.org/10.1101/2020.06.08.20126029 doi: medRxiv preprint World Health Organization et al. 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