May 8th. A large part of the discussion related to how the Covid-19 outbreak will evolve is based on a set of crucial epidemiologic models. Among those, the most classical one is the S-I-R model (« S » for susceptible, « I » for infected and « R » for recovered), which tells that the dynamics of the disease is closely related to the basic reproduction rate, \(R_0 = b/y\) where \(b\) is the rate of effective contacts between the infected and the susceptible, and \(y\) is the rate at which infected individuals recover.
In particular, for the Covid-19, the rate of infection seems at least twice faster than recovery (\(R_0>2\)). Furthermore, complex cases requiring hospitalisation in intensive care are large enough (between 15% to 20% of infected cases), to both create a pandemic explosion and a major risk of excess demand for healthcare. In consequence, the SIR model has implied that a more or less stringent lockdown is required to slow the curse of the disease. If we note by « a » the parameter of lockdown, this is equivalent to build a bridge between the basic reproduction rate \(R_0\), and the effective rate, so that \(R = R_0*(1-a)\), with \(0< a <1\) is a measure of intensity of social distancing success.
Different analyses suggest that for countries which had opted for lockdown, this has been very effective, with \(a=0.64\) for Belgium (see my previous post); \(a=0.8\) in France (see Angot, 2020), and \(a>0.9\) in the case of Wuhan in China (Lin et al., 2020). But, at the time when we go to a relaxation of the rules of the lockdown, the dynamics of « a » added to the S-I-R model may be crucial to re-assess. What if some susceptible people feel that the outbreak of Covid-19 is controlled, and they start now to over-compensate with more social contacts? What if people feel that economic risks are too high versus the cost of being infected, and decide to go back to work without many protections (not necessarily that they wil not try to self-protect, but the availability of masks may remain limited, etc)?
Thus, individuals will be the ones « in fine » to make \(0 < « a » <1\), high enough for a sufficiently long time to crush the pandemic, with little room for Covid-19 to come back as a revenge, in a new wave. In general, we may think that « a » will naturally decrease for the susceptible with time, as the higher the number of infected, the higher expected cost of the disease if infected. This behavior is possible, but the pace of increase in « a » is likely not enough to avoid the heath care crunch (see also Bethune, and Korinek, 2020). For a significant and structurally long term decrease in « a », we need more, and possibly some incentives.
Regarding incentives, the economic theory of moral hazard is a good avenue to look at designing optimal incentives. One example of (negative) incentives is to tax inadequate risky behavior. In the case of Taiwan, it looks like the penalty for infringement has been put at the expected value of a lost life from Covid-19, as result of misplaced social behavior, - and whether you are contagious or not. In the spirit of optimal theory, this multi-thousands money fine aims to have people fully internalizing the risk by making people pay for the ex post materialisation of risk.
Today, many actions launched by governments, during or after lockdown can be tested through the theory of optimal (dis)incentives. But usually, this is not done. Rather, the idea has been to hope for the best, that is, governements keep recalling people of their « moral obligations » to comply with distancing rules. While necessary, it is by far not sufficient, and is clearly important that we know more about how individuals perceive the disease and its evolution, and how they react to consequences of pandemics and policiy actions, be it for health and for socio-economic reasons, to design such incentives.
While we defer a post to this later on, we are here more concerned as to what citizens do and think, so that we have a clear basis as to how to thing about the right focus of incentices. Surprisingly, the data remain sparse.
We have collected a few data, courtesy of Neurohm, from a survey being rolled out across a large set of countries worldwide on the Covid-19 situation. The interesting element of the data is that AI is used in order to ensure a base line of probing survey answer, so that we only use survey answers that look like sufficiently solid for the findings below (see here). We here use France as an example, via a sample of 1,300 individuals. The data below may have some bias, so we caution that we should not be taken the findings as fully representative. For example, we find that 0.8% of the sample population claims to have been positively tested. This figure is higher than currently reported in France (roughly 0.3% of population). But the idea is also to show how crucial it is to understand behaviors and behavioral changes, - and rather quickly, to secure the crush of the disease.
Behavior at time of Covid-19
Here are five facts of importance we collected:
Finding 1: Own and collective infection perception match
We know that the disease is difficult to be diagnosted, with formal test. We find that the perception of being infected by the disease, is large (about 9% outside testing), but this also is quite close to how people report on their knowledge of third parties being (said to be) infected in one citizen’s community. Otherwise, stated, expectations are likely built as a convergence between personal and social perceptions, in line thus with the SIR model that the dynamic of contagion is linked to the stock of infected.
Finding 2: Voluntary reduction in social contagion expected to be > 35%
Based on epidemilogical data, and supposing that there « a > 0 » is only linked to imposed lockdown, simulations suggest that lockdown effective at 50%, will stabilize the outbreak if imposed for a period in the range of 50 to 80 days. The total span of the disease may be then be close to 6 months, at which time the disease dies out (see Alvarez et al., 2020). As discussed above, however, the good news is that individuals may be increasing protection with the disease, so that benefits of lockdown is not fully lost and the pandemic may be finishing faster and with lower infections.
At the time of survey in France, the individuals were already about 2 months in the pandemic. But looking at their expectations on the likely extra duration for the outbreak to disappear, the average is above 1.5 months extra, for a doubling of people being infected, versus the current perception of 11%. Calibrating the risk of getting the Covid-19 to the expected cost of life, so that susceptible people reduce their exposure intentionally without lockdown measures, and using the S-I-R model, we find that the above is compatible with « \(a=0.26+0.7* portion\ of\ Infected\) » going forward, leading to an effective reproduction rate decline to \(R_t=0.7\) at the time the disease fully dies out, and \(a=36%\) (Figure 1)
Figure 1: what “a” to anticipate from survey expectations?
Finding 3: Typical behaviors barriers well, but not perfectly understood/accepted
Reducing the rate of effective contacts can be done through a large set of behaviors, among which washing hands, etc. In general, we find that a population adhering to a few protective behavior may indeed make a growing to 40-50%, pending obviously on the availability of supplies (eg availability of masks, etc). The data survey clearly show that the bulk of, but not all individuals have understood the importance of those behaviors. In fact, while 90% clearly see the danger linked to the disease, 80% actually clearly state that washing their hands is key, and fewer than 60% understand the home insulation, the importance of mask wearing, or restrictions in public transport.
Assuming that people acknowledgement leads to behavior, a would just indeed just go up to 30%. However, this may be far stretched - if behavior is done in 2/3 of cases (as often noticed in behavioral studies), the self protective mechansims will not be enough to match the expectations of the population, and would be also relatively « tied » to ensure that the disease does not have a second wave.
Finding 4: Average is not necessarily representative
The above has looked at the average, but the distribution may be skewed in terms of perception. Regarding the expected duration of the disease, 40% said that the pandemic has been crushed already, for a median that is less than 3 weeks, or more than two times faster than the average. To get to this figure, and number of expected extra infection at the median, « a » will need to double from 0.25 to 0.50, which is not likely to happen based on finding 3, as the protective behavior importance is also reduced at the median by about 25% versus the average.
The risk here is that some part of population do have too optimistic behavior—which may lead to failure of expectations and a disease that will last longer.
Finding 5: the importance of social circles
If our curse is related to our social behavior, we may also see how social consideration may play to counter-act the wrong behavior. Here is a good news: close circles health is as important, if not more, than own health on average. In particular, people are especially worried about the health of old members of their families and about their children health. Also important, people worry about their own citizens for 60% of cases Figure 2.
Figure 2 - self or third party caring?
The above data are usually not available - but they bring a key message. When we get out of the lockdown, we will need to make sure we track (and guide if any) people behaviors to ensure to crush the disease. Self- interest, of possibly, third party interest may be already a good incentive to reduce social contacst, but it is likely to be not enough to navigate through the disease. We need to create a dynamic dashboard on how people may think and act along the way - without this, drivers to ex post measures of recovery, infections and the like, may not be understood, or understood too late versus the fight of the pandemic we still need to have.
The french data also make clear that a few assumptions made in the literature are too simplistic. Do not think average, as the distribution of beliefs and behaviors do not obey a typical distribution; do look at how people loop back social circles to influence their behaviors and beliefs; do not hope for the a sustained reduction as close to the lockdown. If we make the point that beliefs are not necessarily biased, one can really infer how people may adapt behavior in the medium term. Their behaviors often do not match the core assumptions of policy makers. In the case of the French data, the fit between compliance to self protection and beliefs of the pandemics suggests that the effort to be driven by the Franch citizens is less than half of what has been triggered by the imposed lockdown.
Alvarez, F. E., Argente, D., & Lippi, F. (2020). A simple planning problem for covid-19 lockdown (No. w26981). National Bureau of Economic Research.
Anastassopoulou, C., Russo, L., Tsakris, A., & Siettos, C. (2020). Data-based analysis, modelling and forecasting of the COVID-19 outbreak. PloS one, 15(3), e0230405.
Angot, Philippe. “EARLY ESTIMATIONS OF THE IMPACT OF GENERAL LOCKDOWN TO CONTROL THE COVID-19 EPIDEMIC IN FRANCE.” (2020).
Bethune, Z. A., & Korinek, A. (2020). Covid-19 infection externalities: Trading off lives vs. livelihoods (No. w27009). National Bureau of Economic Research.
Lin, Qianying, Shi Zhao, Daozhou Gao, Yijun Lou, Shu Yang, Salihu S. Musa, Maggie H. Wang et al. “A conceptual model for the outbreak of Coronavirus disease 2019 (COVID-19) in Wuhan, China with individual reaction and governmental action.” International Journal of Infectious Diseases (2020).
Leung, K., Wu, J. T., Liu, D., & Leung, G. M. (2020). First-wave COVID-19 transmissibility and severity in China outside Hubei after control measures, and second-wave scenario planning: a modelling impact assessment. The Lancet.
©Jacques Bughin. All errors mine.