Quantifying the intensity of the coronavirus outbreak and its pandemic potential

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A number of groups have estimated R0 for the new coronavirus, meaning that it will die out. But scientists from the Chinese Academy of Sciences Institute of Automation and the University of Chinese Academy of Sciences have estimated R0 to be much higher, at 4.08, indicating great potential for spreading.

Joseph Eisenberg, professor and chair of epidemiology, University of Michigan writes in The Conversation that if you saw the 2011 movie “Contagion,” about a worldwide pandemic of a new virus, then you’ve heard the term R0, pronounced “R naught,” this isn’t just jargon made up in Hollywood. It represents an important concept in epidemiology and is a crucial part of public health planning during an outbreak, like the current coronavirus epidemic spreading outward from China.

Scientists use R0 – the reproduction number – to describe the intensity of an infectious disease outbreak. R0 estimates have been an important part of characterizing pandemics or large publicized outbreaks, including the 2003 SARS pandemic, the 2009 H1N1 Influenza pandemic and the 2014 Ebola epidemic in West Africa.

The formal definition of a disease’s R0 is the number of cases, on average, an infected person will cause during their infectious period.

The term is used in two different ways. The basic reproduction number represents the maximum epidemic potential of a pathogen. It describes what would happen if an infectious person were to enter a fully susceptible community, and therefore is an estimate based on an idealized scenario.

The effective reproduction number depends on the population’s current susceptibility. This measure of transmission potential is likely lower than the basic reproduction number, based on factors like whether some of the people are vaccinated against the disease, or whether some people have immunity due to prior exposure with the pathogen. Therefore, the effective R0 changes over time and is an estimate based on a more realistic situation within the population.

It’s important to realise that both the basic and effective R0 are situation-dependent. It’s affected by the properties of the pathogen, such as how infectious it is. It’s affected by the host population – for instance, how susceptible people are due to nutritional status or other illnesses that may compromise one’s immune system. And it’s affected by the environment, including things like demographics, socioeconomic and climatic factors.

For example, R0 for measles ranges from 12 to 18, depending on factors like population density and life expectancy. This is a large R0, mainly because the measles virus is highly infectious.

On the other hand, the influenza virus is less infectious, with its R0 ranging from 2 to 3. Influenza, therefore, does not cause the same explosive outbreaks as measles, but it persists due to its ability to mutate and evade the human immune system.

Demographer Alfred Lotka proposed the reproduction number in the 1920s, as a measure of the rate of reproduction in a given population.

In the 1950s, epidemiologist George MacDonald suggested using it to describe the transmission potential of malaria. He proposed that, if R0 is less than 1, the disease will die out in a population, because on average an infectious person will transmit to fewer than one other susceptible person. On the other hand, if R0 is greater than 1, the disease will spread.

When public health agencies are figuring out how to deal with an outbreak, they are trying to bring R0 down to less than 1. This is tough for diseases like measles that have a high R0. It is especially challenging for measles in densely populated regions like India and China, where R0 is higher, compared to places where people are more spread out.

For the SARS pandemic in 2003, scientists estimated the original R0 to be around 2.75. A month or two later, the effective R0 dropped below 1, thanks to the tremendous effort that went into intervention strategies, including isolation and quarantine activities. However, the pandemic continued. While on average, an infectious person transmitted to fewer than one susceptible individual, occasionally one person transmitted to tens or even hundreds of other cases. This phenomenon is called super spreading. Officials documented super-spreader events a number of times during the SARS epidemic in Singapore, Hong Kong and Beijing.

A number of groups have estimated R0 for this new coronavirus. The Imperial College group has estimated R0 to be somewhere between 1.5 and 3.5. Scientists from the Chinese Academy of Sciences Institute of Automation and the University of Chinese Academy of Sciences have estimated R0 to be much higher, at 4.08.

These differences are not surprising; there’s uncertainty about many of the factors go into estimating R0, such as in estimating the number of cases, especially early on in an outbreak.

Based on these current estimates, projections of the future number of cases of coronavirus are fraught with high levels of uncertainty and will likely be somewhat inaccurate.

The difficulties arise for a number of reasons. First, the basic properties of this viral pathogen – like the infectious period – are as yet unknown.

Second, researchers don’t know how many mild cases or infections that don’t result in symptoms have been missed by surveillance but nevertheless are spreading the disease.

Third, the majority of people who come down with this new coronavirus do recover, and are likely then immune to coming down with it again. It’s unclear how the changing susceptibility of the population will affect the future spread of infection. This is especially important in Wuhan, the origin of the epidemic.

Finally, and likely the most important reason, no one knows the future impacts of current disease control measures. Epidemiologists’ current estimates of R0 say nothing about how measures such as isolation or quarantine efforts will influence the virus’ future spread.

A Worldometers report looks at how to correctly calculate the mortality rate during an outbreak.

The case fatality rate (CFR) represents the proportion of cases who eventually die from a disease. Once an epidemic has ended, it is calculated with the formula: deaths/cases. But while an epidemic is still ongoing, as it is the case with the current novel coronavirus outbreak, this formula is, at the very least, naïve and can be misleading if, at the time of analysis, the outcome is unknown for a non-negligible proportion of patients.

In other words, current deaths belong to a total case figure of the past, not to the current case figure in which the outcome (recovery or death) of a proportion (the most recent cases) hasn’t yet been determined.

The correct formula, therefore, would appear to be:
CFR = deaths at day.x / cases at day.x-{T} (where T = average time period from case confirmation to death). This would constitute a fair attempt to use values for cases and deaths belonging to the same group of patients.

One issue can be that of determining whether there is enough data to estimate T with any precision, but it is certainly not T = 0 (what is implicitly used when applying the formula current deaths / current cases to determine CFR during an ongoing outbreak). Let’s take, for example, the data at the end of 8 February, 2020: 813 deaths (cumulative total) and 37,552 cases (cumulative total) worldwide.

If we use the flawed formula (deaths / cases) we get: 813/37,552 = 2.2% CFR (flawed formula). Instead, even with a conservative estimate of T = 7 days as the average period from case confirmation to death, we would correct the above formula by using 1 February cumulative cases, which were 14,381, in the denominator: 8 Feb deaths/1 Feb cases = 813 / 14,381 = 5.7% CFR (correct formula, and estimating T=7).

An alternative method, which has the advantage of not having to estimate a variable, cited previously as a simple method that nevertheless could work reasonably well if the hazards of death and recovery at any time t measured from admission to the hospital, conditional on an event occurring at time t, are proportional, would be to use the formula: CFR = deaths / (deaths + recovered), which, with the latest data available, would be equal to: 910 / (910 + 3,324) = 21% CFR (worldwide).

If we now exclude cases in mainland China, using current data on deaths and recovered cases, we get: 2 / (2 + 44) = 4.3% CFR (outside of mainland China).

The sample size above is extremely limited, but this initial discrepancy in mortality rates, if confirmed as the sample grows in size, could be explained with a higher case detection rate outside of China, especially with respect to Wuhan, where priority had to be initially placed on severe and critical cases, given the ongoing emergency.

As the days go by and the city organises its efforts and builds the infrastructure, the ability to detect and confirm cases should improve. As of 3 February, for example, the novel coronavirus nucleic acid testing capability of Wuhan had increased to 4,196 samples per day from an initial 200 samples.

A similar discrepancy in case mortality rate can be observed when comparing mortality rates, as calculated and reported by China NHC: a CFR of 3.1% in the Hubei province (where Wuhan, with the vast majority of deaths is situated), and a CFR of 0.16% in other provinces (19 times less).

Finally, we shall remember that while the 2003 SARS epidemic was still ongoing, the World Health Organisation (WHO) reported a fatality rate of 4% (or as low as 3%), whereas the final case fatality rate ended up being 9.6%.

The WHO had mentioned 2% as a mortality rate estimate in a press conference on Wednesday, 29 January, 2020. However, they specified that this is a very early and provisional estimate that may change. Surveillance is increasing, within China but also globally, but at the moment: We don’t know how many were infected (“When you look at how many people have died, you need to look at how many people where infected, and right now we don’t know that number. So it is early to put a percentage on that.”).

The only number currently known is how many people have died out of those who have been reported to the WHO.

It is therefore very early to make any conclusive statements about what the overall mortality rate will be for the novel coronavirus, according to the WHO.

The Conversation report

Worldometers material

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