Selectivity versus Reach : Flattening the curve of Covid 19 for joint health and economic prosperit

April 8. By April 7th, the number of recorded infections by the covid 19 has passed the bar of 1,5 million individuals worldwide, and likely 75,000 deaths, according to Worldometer’s compiled statistics (2020), while driving a joint health and economic crisis feared to be like "no other,” according to a statement made by the head of the IMF Managing Director, Kristalina Georgieva during a recent IMF-WHO press conference in early April (2020)

In effect, the current virus which originated in China, has now spread to as many as 200 countries worldwide, leaving virtual no one safe. It has put hospital systems struggling to cope with the flow of heavy infected cases, as feared by Richard Baldwin in a recent post on Vox (2020). Hospital, human, equipment as well as ICU beds capacity has been under excess demand rapidly in a course of 3-4 weeks at the outbreak in Wuhan by end of January requiring the import of many health workers into the city, as well as the build up of extra bed capacity in a record time of a few weeks. More recently, the same pressure on health system was apparent in Northern Italy and France, by mid March . The consequence of that is that those countries suffer a higher fatality rate and a slower recovery rate of contaminated people than average, while its medical resources are alas witnessing high toll of illness and excessive stress levels (see Day (2020), Fang (2020), or Bughin (2020a)). 

Containment for all

In parallel, many countries, in face of large uncertainty regarding how the virus behaves, have taken a radical approach to imposing major economic standstill in the hope to flatten the epidemic curve of covid 19. This standstill usually has started by forbidding large crowd meetings (theatres, mega -events, etc). It moved quickly to closing schools and asking people to work remotely, then the ask went to have the population at large go on quarantine in the hope of reducing harmful contacts. 

The fundamental issue is not that a suppression strategy is not appropriate; on the contrary, we must emphasize, this is rather a powerful response to the first wave of an unknown pandemic emerging globally. There is emerging evidence, that if measures are followed by population, it may control the pandemic deployment, as well as buy time for improving hospitals’ and healthcare system supply chain management. It also buys time to know more about the lethal, contagion and incubation features of the Covid 19, and to work on means to battle it viathe discovery of powerful antiviral and vaccines, as well the training of other prevention and monitoring tools.

But it is also true, that a suppression strategy is not sustainable at term, as it creates a growing conflict between health solidarity and economic prosperity. Furthermore, from a social perspective, it will be very difficult to assume that people will remain ok with significantly reducing their close contacts for long, especially when today, there is (at least) a perception, among others given by recorded statistics, that 90 to 95% of the population is “only” being contaminated. Further, it is known from past behavioral studies that people have an increasingly bad feeling, of the burden of prolonged quarantines ( Eg Person et al, 2004). 

How to win in a containment for all strategy?

At the end of the day, the fundamental question remains as to what are the key value parameters that one needs to monitor, in order to create a more flexible model of containment, which still allowing to flatten the curve before the population is possibly immune. One simple way we look at, here, is to understand the various key drivers of Rt, or the reproduction rate through time. Herewith, we have built a simple formulation of Rt to provide as sense of the drivers, as synthesized by the following equation (1).

Rt = Ro *(1/((1-ut)d+ut)))* (rt* (1-srt)*(1-It/Nt) exp(er)+ (1-rt)* b* (1-st)*(1-It/Nt) exp(e))                                                            (1)

Where t is a time period, and R0 is the so-called epidemiologic reproduction rate of the Covid 19, as initiated by Kermack and McKendrick, (1927) .

We further have the following five key parameters :

a)      Getting the distribution skewness right for a disease has significant impact on the potential estimate of diffusion. To account for this, we posit: 0<u<1, where 1-u the portion of superspreaders, and d>1 is a multiplicateur effect. For instance in the case of a Pareto distribution of infection, b=16, and thus the term (1-u)d+u=4, reflecting that the network asymetry reduces the power of spread to the population significantly . We do not know the exact distribution linked to the covid 19, but we have a glimpse from triangulating from other virus distributions of contagion. Measles infection looks like a Pareto distribution; the top 20% typically contribute like 87% for SRAS, while the figure is 93% for HIV (Lloyd Smith et al, (2005). For influenza, the distribution looks more like top 20% makes 50% of the secondary infections (Brauer, 2019). 

At this level of infliuenza, the term (1-u)d+u=1,56. As typically, one estimates R0^ from observed data that embed the effect from the distribution asymetry, we thus need to correct for that downward bias. For an estimate R0^ , say of 2.0, the true Ro will then be more like 3,6. If furthemore, one can selectively target the portion (1-u), and get 50% of the them isolated ( or 10% of population), then the term (1-u)d+u declines to 1,28, or Rt by 18%. This effect is twice bigger than isolating 10% of any average individual, not a small, but not a very drastic reduction due to more uniform distribution of influenza virus. 

b)     Many countries have been in short supply of testing capacity, while also claiming that tests in the markets to date are suffering from low specificity. Thus, the majority of countries, at the exception of Asian countries, did limited testin. Often ,they reallocated the available stokc of tests, for those emergency cases showing up at hospitals to sort out real cases from others.                                                                

We posit : 0< r <1 where r the portion of recorded infected cases to total cases. This figure will of course vary through times. At the outbreak of the virus, it might start to be close to zero. This is especially true in the case of the covid19, where the average combined incubation and contagion period may be around 20 extra days; r is also likely increasing with time, as pre-symptomatic cases become ill, and countries build up more testing capacity and selectivity. We have attempted to have an idea of the actual range of value for r. We have estimated r to be in the range of 10% to 20% by March 20th, for most of European countries after 4 weeks in the pandemic implying that a significant amount of cases have been unrecorded (Bughin, 2020b). Li and colleagues (2020), come to the same conclusions for the case of Wuhan, conclusing that those non recorded cases may be responsibile for a rather rapid dissemination of novel coronavirus.

c)      What drives contagion is the number of close contacts, due to the mechanisms of entries of the virus into the respiratory system of individuals. We posit ; 0<s(r)<1 where s(r) is the portion of reduction in contagious social contacts for (un)recorded contaminations. This reduction is of course a weighted average of actions between different sociodemographic segments—for example, someone in its late thirties, who has a front line sales service jobs, one teenager kid at high school, and a good social lives, might have roughly 5 times more contacts than a retired single person of 60 years old, according to our computation. In general, also, older persons’ contacts become only social in a closely tight community setting, making them more at risk, but less contagious given close networksn, while young adults have all sources of, and all types of close contacts possible, -friends, work, school kiss and drives, concerts, parties, love partners, etc. In effect, school and work contact are roughly 40% of total contacts,, 1/3 other is from community circles, and the balance is from own family. By closing school and work in their fight to covid 19, most countries put themselves in the better position to have s(r)>0,5.

Getting sr larger than 0,5 is however challenging at the household level, (we look at the household level, because social distancing involves closer and more frequent contact within the household, but by breaking their external tie, the contagion is stopped). This is because some work from front lines remain necessary in cirtical sectors, such as healthcare, equipment manufactruring and food,logisitc and pharmaceutical services for instance, for a total of typically 25% to 30% of a typical developed economy. This is also because people are usually not fully compliant with soical distiancing. In fact, most academic studies suggest that contact rates for non infected individuals, tend to decrease by 30 to 40% during period of large influenza, but this is rarely higher, if not strictly imposed. (see Caley, et al 2008). 

d)     It/Nt is the ratio of infected cases, It, in susceptible population Nt, at time t, and we posit that e(r)>0 where er is a proxy for risk aversion into the economy, and which plays out as a multiplier on extra caution taken by the population as far as the contagion spreads into the economy.

There is evidence of e(r) being large. For example, during the 2002 SARS, more than 25% of Asian citizens thought they could be contaminated, even if the ex post rate happened to be less than 0.1% ; as a result, travel was reduced significantly, (10 to 50 percent declined in taxi revenues, and up to 80 percent reduction in hotels stay, see Brahmbhatt and Dutta, 2008. Likewise during the 2019 H1N1 outbreak, 25% of Americans were avoided crowded area (Steelfisher, et al, 2010). For a flu-type, and provided consumers act rationally, frequency might change downward, with a resulting reduction of the attack between 20 to 40% ( Tyson, et al 2020).

e)     We finally posit 0<b(<1), where b is the ratio of the level of contagion of non recorded cases. We note that b is linked to milder cases or asymptomatic cases of the Covid 19. There are only a few studies trying ot estimate b, and they seem to conclude that b might be in the range of 0.4- 0.5 for Covid 19 (see Li, et al. 2020). The actual value of b is likley to be driven by the portion of asymptomatic cases, versus others, which contagion period may last 20 days, while it is only 10 days for the people moving into hospitals and in their houses (and they are being quarantined). If the portion of asymptomatic cases may be as large at 50%, b is likely to be in the range of 0,4 to 0,6. Those rate of asymptomatic to total cases have been noticed in fullly tested population like the village of Vo in BNorthern Italy, or in the cases of random sampling in South Korea and Belgium hospitals testing any patients in hospitals.

We have played with the five parameters above, after calibrating the data to Belgium as of April 1, at the time Belgium had recorded just below 14,000 covid-19 infections, and suffered 828 hospital fatalities. Belgium has been a country with relatively fast decision to go to major containment, -already after the 10th recorded death at hospital, but is suffering from supply chain scarcity, as well as from testing the susceptible population at scale. It does not trace people, yet it may be looking at possible means at current stage.

If we look at the daily change of recorded cases and fatalities, on that day, Belgium recorded cases might imply that the pandemic could have been spreading,like the flu (R0=1,3) by April 1 . Crude estimate based on recorded cases implies that Rt looks like 1,5, but the above eqution (1) suggests this is possibly biased downwards. Using the flu asymetry of contagion, Rt= 2,55, without considering the possibility of non recorded cases . Evidently, recorded infected cases do not include all the full cases, as Belgium has had a limited testing policy, with about just above 6/1000 of population tested by April 1. Another way to know the biases linked to unreported case is to compute Rt on number of deaths. If one assumes constant fatality rates, then the logic may hold and we can estimate, from the march data, that Rt>1, Rt=1,7, or a true R0 in the range of 2,6. 

We have computed R0 for three assumptions of infected cases, eg with r=0,7 ; r= 0,2, and r=0,1 by April 1 ; Ro is computed up to March 18th before the containement measures. Assuming that d>1 is like the influenza, we compute that the « true » R0=3,8 for r=0,7 ; R0=2,7 for r=0,2, and R0=2,55 for r=0,1. Not surprisingly, R0 decreases with higher r, as simply this implies a large volmue of infections, especially at the start, flattening the real curve of infection. Note finally that the R0 computed from fatalities is closer to the one we have for low r, which is consitent with the idea that recorded cases is likely undescoring true cases of infection by a factor of 10, just before the containment measures were announced in Belgium. 

Our simulation is based on the following discrete values : s =0,4 and s=0,8 ( noting that s=0,8 is difficult to achieve without very strict, Asian like rules, let alone to have the effort sustained after 6 weeks; b= 0,4 and b = 0.6 , as well as e=20,100. The later value of risk aversion has been computed from different studies in Asia, but the parameter value is also dependent on protective equipment to sustain aversion behavior ; in particular, Belgium is missing mask protection.

Table 1 presents the results, based on one critical assumption that unrecorded cases have 5 times lower probability to go to hospitals long term, than recorded cases. This is based on the assumption that, most likley (see above) r=0,1 to 0,2 ; meaning there were roughly 100,000 cases in Belgium by March ended, from 13500 recorded cases (and 4500 tested). Given that asymptomatic cases tend to be 50% of total, we have 50,000 each (a) symptomatic cases. For symptomatic cases, using the Chinese numbers, of 13% with risk that requires hospital health care, we reach 6500 cases to go to hospitals, ten days later (contagion time of 20 days). Today, we have roughly 11000 hospitalisations sicne the start of the outbreak, thus 6500 cases for 13500= 48% admissions for recorded cases, and 4500/36500=12% for unrecorded symptomatic cases, or 4 times lower rate of hospitalization. 

As we wish to look at sensitivity regarding r, we present th two extremes case of r=0,1 (most likely) and r= 0,7 (current understated cases) . We also compute the implied hospital ICU capacity, as the last column, based on a capacity of 2500 ICU beds. The results in Table 1 are very clear, in that :

a)     The main driver among the 5 variables discussed is reduction in social contacts, s(r)

b)     Peak of infection, as well peak in hos)ital based fatalities both emerge by mid April and are compatible with ICU supply, when social contacts are on average reduced by more than 50%

c)      Accounting to a large unaccounted cases ( r=0,1), with lower fatality and lower contamination, may crowd out the risk of the pandemic, as the true R0 is actually lower than thought

d)     Risk aversion, e  exerts a significant protection to pandemic development, but the factor is an order of magnitude lower than social contact, eg two to two times lower effects of contagion and casualities

e)     Superspreading, d, plays a role, but especially when risk aversion as well as contact reductions are limited- alas, at that time ICU capacity is already hit

f)       b is also an important, yet secondary driver, of contagion effect, with a higher b leading to more infections and casualties

Table 1.- Belgium SEIR model for covid 19, rollout from April 1, 2020

A « moving target » for Belgium in the case of all containment

Note that Belgium range of values should be in the range of r=0,1 ; s= 0,45 ; b=0,4 ; e=25, and u=90%. At this level, Belgium might reach 145,000 total infections by May 1rst, about 2200 hospital deaths for an ICU utilisation at 90% of capacity. However, the peak in recorded daily infections is not happening before May 1rst, yet it peaks roughly between April 17 to April 21 for number of daily fatalities . Still, a slight marginal deterioration in performance regarding any of the parameters quickly leads to higher casualties and ICU being > 100%, highlighting the importance of active policies to cope with the Covid=19.

Further, based on the simulation above, and run of Monte-Carlo across large range of the data, we confirm that reduction of contagious interaction, s, is the main first order, then superspreader identification, u and increased self protection, e. This data range implies that, in the absence of specific targetting, and only testing at time of hospital venue, we should aim for a reduction of 50% of interaction both to flatten the curve, and be compatible with health constraints ; further increased protection must be large enough (e>20), with people washing hands frequently and use mask protections.

From reach to selective testing, tracing and enforced quarantine

One can directly derive from above, that a reduction of contact by 50% is difficult to hold, without some imposed shut down of education and work, and for a long time (minimum 2 months). Hence, it implies a few additional strategies , when economies are to be relaunched :

a)      telecommuting, must become a standard of practice going forward

b)     Public protection must become the new normal, eg in Asia, most restaurants require you wash hands, most malls have hydroalcohol gel at their entrance to be used etc

c)      But the most important is the priority of systematic testing of the infected and their close social ties upfront , to put them in quarantine. 

Regarding the last point, we resorted to simulation to show the logic, based on Belgian figures for the Covid-19 pandemic, see Figure 1.

Figure 1- selectivity versus reach in containment , from Belgium data

Without targetting, we must impose 50% social contact reduction to anyone at minimum to control the pandemic and cope with the Belgian heathcare constraints. We have thus no choice but to shutdown the economy as a large set of contacts are related to education and work.

When doing this, we hurt citizens prosperty. At minimum, with current R0 and no forced measure, 36% will be affected in two months, and 100%-36%=64% of citizens, may feel to have done a « worthless » economic effort during those 2 months. ( Of course, by their commitment, at 50% reduction of contacts, they may have flattened the curve from 36% to 7%, a factor of 5, and saved the hospital system for the coming months, where 80% of them will be affected by the virus. ( note : z=80% is the result of solving R0+(1/z)*log(1-z)=0).)

Now, consider we can target effectively the contaminated individuals. To the extent that we have a way to spot them with specificity above 70%, and that their close ties like them are being put in strict quarantine at 100%, (and, if first test fails, any infected social ties will be tested positively and by social link, the source will also be spotted), the solution is both more effective in flattening the curve, beyond the constraints of the hospital sector, and without to have lots of people not being used as workforce in the economy. 

The new social norm of being traced

We understand that test specificity must be large enough, as it is not clear we can with high asymptomatic cases. We might have to do a mix of both approach in those circumnstances, even if today, asymptomatic cases may have low contagious power ; and evidence shows that medical and non medical testing combined may make the target of 70% possible ( Alibaba claims that its AI-based applications have success at 95% ?). 

We also understand that tracing individuals can be done through mobile and bluetooth/ Beacon like technology, but this must be done with extreme caution (Christoph and Gunther, 2020). However, given the large externality of contagion, this tracing is likely to be raised as an important social norm to comply in order to accept in order to reconcile health and economic prosperity

In practice, this path has been shown today by countries such as Singapore or South Korea, to be the best to control the covid 19 pandemics to date (Anderson et al, 2020). In those cases, data were anonymized to other citizens, and we might think of a civil society governance model for data crunching that preserve privacy and GDPR compliance. It is time to make this happen as AI, big data, 5G and other digital technologies may become a great complementor to our society ( Pissarides and Bughin, 2019).

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