Wednesday, September 03, 2014

PLoS Currents: Calculating An R0 For Ebola


R0 (pronounced R-nought) or Basic Reproductive Number.

Essentially, the number of new cases in a susceptible population likely to arise from a single infection. With an R0 below 1.0, a virus (as an outbreak) begins to sputter and dies out. Above 1.0, and an outbreak can have `legs’.


# 9033


One of the crucial pieces of information epidemiologists and statisticians seek on infectious diseases is just how contagious is it?   Some viruses – like measles – spread like wildfire through a susceptible population, and a single person may pass the disease on to another 12 to 16  people.

Others, like MERS-CoV and the avian flu viruses, appear to have very low R0s – less than the 1.0 requisite to sustain an epidemic.   Those numbers could change, of course, should these viruses adapt further to human physiology.


With the Ebola outbreak being described by the CDC director as `spiraling out of control’ in West Africa there is a lot of interest in the rate of spread, or R0 of this epidemic. To that end, Christian L. Althaus, a mathematical epidemiologist with the University of Bern, has been crunching the numbers to come up with an estimate of Ebola’s Basic Reproductive number.


This from PloS Currents Outbreaks.


Estimating the Reproduction Number of Ebola Virus (EBOV) During the 2014 Outbreak in West Africa

September 2, 2014 · Research

Christian L. Althaus


The 2014 Ebola virus (EBOV) outbreak in West Africa is the largest outbreak of the genus Ebolavirus to date. To better understand the spread of infection in the affected countries, it is crucial to know the number of secondary cases generated by an infected index case in the absence and presence of control measures, i.e., the basic and effective reproduction number. In this study, I describe the EBOV epidemic using an SEIR (susceptible-exposed-infectious-recovered) model and fit the model to the most recent reported data of infected cases and deaths in Guinea, Sierra Leone and Liberia.

The maximum likelihood estimates of the basic reproduction number are 1.51 (95% confidence interval [CI]: 1.50-1.52) for Guinea, 2.53 (95% CI: 2.41-2.67) for Sierra Leone and 1.59 (95% CI: 1.57-1.60) for Liberia.

The model indicates that in Guinea and Sierra Leone the effective reproduction number might have dropped to around unity by the end of May and July 2014, respectively. In Liberia, however, the model estimates no decline in the effective reproduction number by end-August 2014. This suggests that control efforts in Liberia need to be improved substantially in order to stop the current outbreak.

(Continue . . . )



Calculating the R0 during an epidemic is always difficult, and given the current limits of surveillance and reporting from the affected areas, there is perhaps even more uncertainty in these calculations than usual. 


The R0 can also change over time, and vary widely between regions, but these numbers are pretty much in line with earlier estimates.


Previously, the R0 for other Ebola outbreaks has been calculated as generally being under 2.0 (see The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda).


R0s are averages, of course,


And as we’ve seen with other outbreaks, some patients are dead ends for a virus, while others (for a variety of reasons, including variations in the pathogen, individual physiology and opportunity) become very efficient spreaders of a disease.

During the SARS outbreak of 2003 (a much more contagious respiratory virus), studies found most infected persons would only infect 1 or perhaps 2 additional people, and sometimes none.  But a small percentage of those infected were far more efficient in spreading the disease, with some responsible for 10 or more secondary infections.


SARS jumped from Asia to North America courtesy of a single superspreader  -- a Chinese doctor who had treated cases in Guangdong  and who stayed at the Metropole Hotel in Hong Kong to attend a wedding. He passed the virus on to roughly a dozen people during his stay, including one who took the virus on to Toronto, Canada.  

Other super spreaders in Singapore, and Toronto, helped give `legs’ to the epidemic.  Without their help, SARS might never have spread beyond Asia.


This super spreader phenomenon gave rise to the 20/80 rule, that 20% of the cases were responsible for 80% of the transmission of the virus (see 2011 IJID study Super-spreaders in infectious diseases).


In January of 2013, in Influenza Transmission, PPEs & `Super Emitters’ we looked at research (InfluenzaVirus: Here, There, Especially Air?) that found a five patients (19 percent) in their study  were "super-emitters" who emitted up to 32 times more virus than did the rest.


Patients who emitted a higher concentration of influenza virus also reported greater severity of illness. 


While Ebola and Influenza don’t spread in the same (airborne) fashion, it is likely that some Ebola patients – particularly those experiencing severe external symptoms (including vomiting, diarrhea & bleeding) – are more likely to transmit the virus than others.

And then there’s opportunity, or being in an environment conducive to infecting others.


The outbreak in Sierra Leone has been linked back to a single introduction of the virus at a funeral last May, when 14 women were infected, and proceeded to pass the virus on to others (see NYTs Outbreak in Sierra Leone Is Tied to Single Funeral Where 14 Women Were Infected).


The introduction of the virus to Nigeria by a single traveler - Patrick Sawyer – led to the infection of a dozen of his direct contacts, many of whom were called upon to help physically restrain him.  And from them, more than a half-dozen secondary cases have emerged, and more may be coming.


Both could be described as `super-spreader’ events, and can serve to drive an epidemic in unexpected ways.


While there is still much we don’t know about the causes of this phenomenon, Stein’s excellent 2011 review Super-spreaders in infectious diseases, explores some of the theories.


What makes a super-spreader?

It is still unclear why certain individuals infect disproportionately large numbers of secondary contacts. Increased strain virulence, higher pathogen shedding, and differences in the host–pathogen relationship were advanced as potential explanations.13, 42 An interesting observation comes from the 2003 Hong Kong outbreak, where a ‘runny nose’, unusual for SARS, was described in a super-spreader, fueling the hypothesis that patients with slightly different symptoms, perhaps as a result of co-infection with another microorganism, could become super-spreaders.43


How much of a role super spreaders will ultimately play in this Ebola outbreak remains to be seen, but experience has shown that they can often have significant impacts, particularly with diseases that under most circumstances, don’t spread readily in a community.

1 comment:

Anonymous said...

Calculating R-nought like this is likely worthless given the poor data quality involved. WHO and western care giver personal testimony indicate the WHO numbers reflect a minimum of 25-50% of reality, especially in Liberia.

It probably is more useful to simply say that infections have more than doubled each week in the more recent reports of the worst affected regions.