We might be winning the battle of the Covid-19 epidemics: a dynamic R0 perspective

March 07. In a series of articles, I recently made the point that under no containment scenario, and assuming a constant reproduction rate, the Covid-19 may bring a) up to 20 million fatalities worldwide on possibly a curse running for about one year, b) as well as a significant damage to economies, especially if risk aversion explodes as it often does during early outbreaks.

Covid 19 went recognized at the end of December 2019, when a Wuhan hospital admitted four ind ividuals from the Seafood Market. Given the exponential contagion during outbreak as it was also discovered at the start of the epidemic at Hunan for the Covid 19,  there has been an absolute case that warrants to act fast- (that is, before the take off of the exponential)-, as well as at scale, (-so that the contagion becomes non self reproducing). The good news is that the world has been facing with many epidemics, and has learned a set of critical actions to battle to curb the diffusion of many diseases, such as Ebola, the SARS and others.

The type of explosion of cases one witnessed at the start of the Covid 19 outbreak made indeed lots of insiders to fear for the worst. In less than one month, from January 20 to February 17, the suspected cases increased exponentially, from 270 to close to 50,000 in the Hubei province, or a factor of 200 ; with a continous doubling of cases every 7 days like in the early weeks of the outbreaks, this could have led to 450,000 infected cases by early April and passing the bar of 5 million before early May.

This gives some amunitions to the risk of 20 million death casualties if things remain constant and are of the Hubei region type of outbreak. But there were some good news, apart from the fact that China outside Hubei region had exponential, but with less power, than theHubein region . Even if it took a few weeks to launch strong actions, Chinese authorities then quickly imposed by mid January, large scale quarantines, as well multiple city shutdowns. Other, more recent actions have involved new series of ways to more accurately diagnose mild cases, as well as the establishment of a mobile based QR code coloring of Chinese citizens to secure more effective sorting of susceptibles, contaminated and sane cases (see https://finance.yahoo.com/news/china-seeks-help-national-tech-110156832.html).

Those actions, in line with our prescriptions needed to maximize the chance to reduce the spread of disease, seem to work, and some are more and more  cautiously optimistic that the pandemic may become most probably than not, controllable and run away its course in China, in the next two months, instead of exploding ( See Lucey, Daniel; Sparrow 2020. "China Deserves Some Credit for Its Handling of the Wuhan Pneumonia". Foreign Policy)

Based on current numbers and the actions taken by China, and in other European countries with outbreaks such as Italy and France, we may be leaning towards a scenario towards a good to severe flu worldwide. The key is thus to continue high vigilance, deliver fast and scalable actions of social distancing, shutdowns if necessary, across the globe when the epidemy is entering a new country. And make sure citizens adapt their social behavior as a significant contributor to curb the disease spread. 

1. What could drive a major pandemic for Covid 19?

 1.1. The three factors

A pandemic size, speed, and risk depend on level of, and spread of population clusters’ reproduction rate, incumbation and contagious period, and fataly rate (see my article at https://www.dhirubhai.net/pulse/three-key-covid-19-indicators-curb-likely-20-million-human-bughin/)

On the positive side for Covid 19, the virus seems to exhibit a strong, but not exceptional high level of the normalized reproduction rate, called R0, (R0 is in the range of 2 for the whole of China, estimated from data january to February, and about 2.7 for same period in the Hubei region). But on the negative, the virus has a material fatality rate (2 to 3%) versus a typical flu, as well as exhbits a possibly less concentrated distribution of social contagion ( in fact, we estimated that the top 20% of infected people from Covid 19 accounted for 55% of total cases, thus superspreaders are affecting up to 6 times more people than others).

The reproduction rate is above 1, fearing an exponential growth, as seen in all regions of China, and now in ealry outbreaks of Europe. But looking again at the figure deeper, another good news is that at an average of reproduction of about 2 in China for the last two months, this mathematically implies that the long tail of 80% of infected would be infecting less than 1 extra person, leading to a rapid decay of the epidemic cases of Covid 19, if one can isolate the superspreaders.

 1.2. Changing R0

 The underlying maths

As the exponential nature of the outbreak is driven by the mean and spread of reproduction rate, R0, it is critical to see how we can limit it.

The estimate R0 has often been (wrongly) perceived in the epidemiologic literature as a constant. This is not the case. The good news is that the reproduction rate R0 is easily interpretable as the product of contact frequency, c and the probability of being contaminated for each contact, p ( see Larson, 207, Simple Models of Influenza Progression Within a Heterogeneous Population,  Operations Research) :

R0 = p.c

p is clearly a variable one can influence, and rather quickly. This implies that R0 may evolve through times, os a result of imposition of quarantines, or still because the population changes behavior in terms of social distancing.

In general, the number of contacts, p, may be constant behaviorally, at least for very low (perceived) risk disease, and for people not aware of the possible pandemic. However, the larger the perceived risk of the pandemic, the more likely citizens may adapt behavior and reduce contact, making R0 decline with time. Changes can include social distancing and other protective measures. 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 a large set of persons were reducing travel (10 to 50 percent declined in taxi revenues, and up to 80 percent delcine in luxury hotels stay, see Brahmbhatt and Dutta, 2008, On SARS type of econoic effects during infectious disease outbreaks, World Bank, Policy research working paper).  Likewise during the  2019 H1N1 outbreak, 25% of Americans were avoided crowded area (Steelfisher, et al, 2010, public's response to the 2009 H1N1 influenza pandemic, New England Journal of Medecine , 362 (22) (2010)

Recent research, accounting from rational expectations made by citizens as to the consequence of being contaminated suggests that it would be rational for any self interested individuals to decrease the number of contacts. For a flu-type, and provided consumers acts rationally,frequency might change downward, with a resulting reduction of the attack between 20 to 40%.  In general, the types of reduction depends on many behavioral éléments and the wisdom of crowd, and the result decline change on p, may be more or less. ( see, Tyson, R.C., Hamilton, S.D., Lo, A.S., Baumgaertner, B.O. and Krone, S.M., 2020. The Timing and Nature of Behavioural Responses Affect the Course of an Epidemic. Bulletin of Mathematical Biology, or still Eksin, et al. 2019. Systematic biases in disease forecasting–The role of behavior change. Epidemics, 27).

Beyond the maths : case studies

We do not know how behaviors have changed in China, as a result of the spread and perception of risk of the spread, of the  Covid 19. But there is enough anecdotal evidence that behaviors have changed for citizens, towards lower contact rates, while authorities in any case forced them towards that consequence.  

If one looks at other outbreaks, and looked at effective reproduction rates ( the dynamics were already mentioned here and there in my previous articles), we found the following ( Table 1), which means that with time passing actions and behaviors may curb the outbreak :

           Table 1 : dynamics of reproduction rates

Outbreak         reproduction rate R0    mid period of outbreak (peak)  late period of

SARS asia                  2.2 to 3.6                     1.6 to 1.8                                0.7

SARS elsewhere         1.6                            0.95                                       

            H1N1                          2.5 to 3                       1.4                                         0.5 to 0.6

           Mexican Flu                 2.1                              1.8                                         0.9

Source: Lit Search, author computation

 SARS and H1N1 were handled with large quarantines, with behavioral changes may explain 30 to 40% ( my rough guess) of the decrease in the reproduction rate through times.

The case of the Mexican flu is a known case of active policy reduction. The flu did spread in multpile villages in the country, but without very large awareness of the inhabitants—leading to a siginifcant attack rate in the range of 40 to 50%. The city of Mexico got the country side flu epidemy noticed and in the first weeks of the flu moving into the country capital, social disitancing was imposed in the first two weeks, but quickly closure measures got enforced on schools, public spaces and hospitals the next two weeks, leading to a significant decline on the reproduction rate.

One concludes that RO may be indeed push downwards from those case studies, and that in general , a) each effect may work, but not eonugh to curb the full pandemic, b) behavorial and policy actions are complementary, thus more powerful to curb outbreaks, c) it must happen early, so as really to avoid the damaing effects of the exponentials.

 2. A Dynamic R0 for the Covid-19 case : we may be winning the curse

2.1. Dynamics of R0 to date for Covid 19 (based on China data)

We do not know the drivers of R0 for Covid 19, but we can estimate its effect, through the shape of how the outbreak has behaved. Using the numbers of contagions, and doing a two weeks by two weeks cut off estimate, we reach the following result that we might have reached a situation of control in China—(see Table 2).

Usually, based on typical contact profiles ( at home, with friends, at work, school), the frequency of contact may roughly be 60% based on public connections (travel, school, at work), and 40% based on personal interactions (with frienss family, etc). China has worked a lot on public contacts reduction ; the fear of the disease has likley play too on the rest of social interactions, it may well seem.

Table 2 : dynamic R0 for Covid 19 in China

Date               Hubei region              rest of China

15 jan             5.5 to 6.0

30 jan              4.0 to 5.5                    2.8      

15 feb             2.5 to 3.5                    1.1                                         

29feb              <1                              <1

Source : wikipedia, John Hopkins University, how computation

Notes : ranges depend on hypotheses on reported cases, and on changes in contagion period

2.2. From a severe flu, rather than a 20 million fatalities: Maybe, we are winning the battle?

It is important that those figures got confirmed, and that the figures do not reflect a one-off, as outbreaks may be re-imported, may have multiple modes, etc. But the key insights too, is that, even if one assumes from now on, that  R0 will be getting indeed just below 1, the total outbreak cumulated by end of year will be more like less than 3-5% of the total population in the Hubei region. For China outside of the Hunan region, the figures will be then less than 0.3% of total population.

Otherwise stated, and scaling those figures to worldwide population, we will be between 0.4 million to 4 million fatalities ( China outside of Hubei, and Hubei) regions. We will have succeeded in controlling the outbreak.

March 07, all errors are mine. comments welcome