Science: How contagious is COVID really? The R0 number… – My Comments

[I have learned that the contagiousness of any disease is referred to by a number called R0 – "R naught". This number means the following: If a person has the disease, this number indicates how many people that person will infect. If the number is less than 1 then the disease will die out. If the number is greater than 1 then it can lead to a pandemic. This number is also based on exclusion factors like whether people have been vaccinated or whether herd immunity has been achieved. Measles, which is highly contagious for example, has an R0 of 18. So what is the number for COVID? This is the latest science paper I could find on the matter. This is from May 2021. According to this the scientists estimate: R0 to be between 3.5 and 6.4. They also estimate herd immunity to only occur when between 71% and 84% of the population has been infected. HOWEVER, if the data they are basing their science on, has been skewed by other junk factors, then all these numbers will be wrong and will be extremely high. So the average for this number, given the above scientific conclusions is about 4.95. Anyhow, here, for what it is worth, is what some scientists wrote. The fact that is it more contagious in the USA – also makes things seem quite dodgy. I've only published the ABSTRACT and the DISCUSSION portion of the document. The full link with charts is sourced at the bottom. Jan]

Estimating the reproductive number R0 of SARS-CoV-2 in the United States and eight European countries and implications for vaccination


We estimate early growth rates of SARS-CoV-2 outbreaks in the US and Europe.

The early epidemic grew exponentially at rates between 0.18 and 0.29/day.

The median R0 value is 5.8 in the US and between 3.6 and 6.1 in other countries.

The herd immunity thresholds are between 71% and 84%.

Individual heterogeneity in protective immunity affects vaccination schedules.


SARS-CoV-2 rapidly spread from a regional outbreak to a global pandemic in just a few months. Global research efforts have focused on developing effective vaccines against COVID-19. However, some of the basic epidemiological parameters, such as the exponential epidemic growth rate and the basic reproductive number, R0, across geographic areas are still not well quantified. Here, we developed and fit a mathematical model to case and death count data collected from the United States and eight European countries during the early epidemic period before broad control measures were implemented. Results show that the early epidemic grew exponentially at rates between 0.18 and 0.29/day (epidemic doubling times between 2.4 and 3.9 days). We found that for such rapid epidemic growth, high levels of intervention efforts are necessary, no matter the goal is mitigation or containment. We discuss the current estimates of the mean serial interval, and argue that existing evidence suggests that the interval is between 6 and 8 days in the absence of active isolation efforts. Using parameters consistent with this range, we estimated the median R0 value to be 5.8 (confidence interval: 4.7–7.3) in the United States and between 3.6 and 6.1 in the eight European countries. We further analyze how vaccination schedules depend on R0, the duration of protective immunity to SARS-CoV-2, and show that individual-level heterogeneity in vaccine induced immunity can significantly affect vaccination schedules.

4. Discussion

In this work, we report rapid COVID-19 epidemic spread before broad control measures were implemented in the US and in the eight most affected countries in Europe during March 2020. We further estimated that R0 values range between 3.5 and 6.4 in these countries, which means high herd immunity thresholds between 71% and 84%. Together with our previous estimates for the outbreak in Wuhan (Sanche et al., 2020), these results are consistent with SARS-CoV-2 being highly transmissible irrespective of heterogeneities in geographic and social settings and emphasize the necessity of strong control measures, such as social distancing. A high level of coverage of effective vaccines are needed to achieve herd immunity. We further show that the heterogeneity of individual-level protection provided by a vaccine is an important factor in determining the frequency of vaccinations.

Awareness of the extraordinary high rates of COVID-19 spread in the absence of control measures is critically important for epidemic preparedness. The short doubling times of the epidemic means that health care systems can be overwhelmed in a couple of weeks rather than several months in the absence of control (Li et al., 2020b). For example, a report shows that the number of COVID-19 patients admitted to intensive care units in Italy during February and early March 2020 grew at a rate of approximately 0.25/day during early epidemic (Grasselli et al., 2020). We estimated that the SARS-CoV-2 outbreaks grew extremely rapidly at rates between 0.18 and 0.29/day, in eight European countries and the US. These estimates for European countries are in general consistent with other studies using different approaches and different sources of data (Dehning et al., 2020, Flaxman et al., 2020, Pellis et al., 2020). We further show that because of the high transmissibility of the virus, moderate control efforts will not sufficiently slow the virus spread to achieve measurable public health benefits. This may explain the continuous growth of the outbreak in some countries despite measures, such as work and school closures, were in place. To delay the peak or to reverse the growth of the epidemic with non-pharmaceutical interventions, strong and comprehensive intervention efforts, such as wide-spread testing, isolation and quarantine, use of personal protective equipment, and social distancing, may be needed.

While we found remarkably high rates of epidemic growth in all the examined countries, we caution that our inference is largely driven by data collected from highly populated areas, such as Wuhan in China, Lombardy in Italy, and New York city in the US. Heterogeneities in the growth rate almost certainly exist among different areas within each country. For example, recent works suggest that the rate of spread is positively associated with population densities (Rader et al., 2020). Therefore, the estimates we provide may represent good estimates in highly populated areas such as in cities.

One limitation of our inference (as well as in other works (Dehning et al., 2020, Flaxman et al., 2020, Pellis et al., 2020, Romero-Severson et al., 2020)) arises from the case and death count data. Case confirmation data is influenced by many factors, including underreporting (Li et al., 2020c). Death and the cause of death are usually recorded more reliably and are less affected by surveillance intensity changes than case counts. However, COVID-19 death counts may also underestimate the true COVID deaths. For example, it is possible that deaths from COVID-19 are underreported when people are unaware of community transmission of COVID-19 (Kong et al., 2020) or when health care system is overwhelmed (Li et al., 2020b). In addition, factors including changes in definitions and protocols for ascertaining COVID deaths, updating prior deaths may also impact on COVID death reporting.

Calculation of the basic reproductive number requires knowledge of the distribution of the length of serial interval (SI), which in turn is determined by the latent and the infectious periods. Similar to our earlier work (Sanche et al., 2020), we assumed parameter values that are consistent with a mean SI of 6–8 days, based on estimates using transmission-pair data from Wuhan, China and Vo, Italy (Ali et al., 2020, Lavezzo et al., 2020, Thompson et al., 2020). This led to higher estimates of R0 for the European countries than other studies (Flaxman et al., 2020, Salje et al., 2020). For example, Flaxman et al. assumed a mean serial interval of 6.5 days according to Bi et al. (2020). However, Bi et al. demonstrated that when the transmission pair is not isolated rapidly after symptom onset, the mean serial interval is estimated to be 8 days (Bi et al., 2020).

Shorter mean SIs were frequently reported in the literature, for example, 4.0 days in Du et al. (2020), 5.8 days in He et al. (2020), 4–5 days in Nishiura et al. (2020), 4–5.2 days in Ganyani et al. (2020). However, these estimates were based on data reported in locations outside of Wuhan, Hubei province, and other Asian countries and territories neighboring China, and thus were strongly impacted by active surveillance and isolation effort as demonstrated by Ali et al. (2020) and discussed in Bar-On et al. (2020). Indeed, we previously estimated that in provinces outside of Hubei province, the mean time from symptom onset to hospitalization/isolation, was as short as 1.5 days after Jan 18th (Sanche et al., 2020), suggesting an exceptionally active surveillance effort. For the purpose of estimating the basic reproductive number, R0, and the herd immunity threshold, the mean serial interval in the absence of isolation effort is the relevant quantity to use. Therefore, we believe our estimation of R0 represent a more accurate estimate. Further work characterizing the heterogeneities of the distribution of serial intervals and measuring serial intervals from individuals who are asymptomatic may help to improve the estimation of R0 (Park et al., 2020).

We calculated the classical herd immunity thresholds 1 − 1/R0, derived from models assuming a homogenous population (Anderson and May, 1991), to be between 71% and 84% in China (Sanche et al., 2020), the US and the eight European countries. These are very high thresholds for random vaccination even with an effective vaccine. A recent survey showed that only approximately 50% of Americans plan to get a COVID-19 vaccine (Mello et al., 2020). Assuming 90% efficacy, 50% coverage only leads to a population immunity of 45%. This is much lower than the herd immunity required to stop transmission. This highlights the importance of public education about COVID-19 vaccination to ensure high vaccine coverage to achieve herd immunity (Mello et al., 2020). Other intervention efforts including both non-pharmaceutical, i.e. effective test, trace and isolation, and pharmaceutical interventions, i.e. therapeutics, are likely needed in addition to vaccination. If the herd immunity threshold is not achieved, i.e. a likely scenario given the high herd immunity thresholds, transition to endemicity will be expected (Lavine et al., 2021).

We note that the herd immunity thresholds derived from the classical formula, 1 − 1/R0, represent good estimates in the context of random vaccinations and recent works pointed out that the disease induced herd immunity threshold may be lower due to heterogeneity in population structure, such as age structure and contact activity levels (Britton et al., 2020), and individual susceptibility and exposure (Gomes et al., 2020). This is because individuals with a high level of contacts are more likely to be infected and once these individuals are recovered/vaccinated and immune, the infectious agent is much less likely to spread. This may be true when there exists substantial heterogeneity in the population and risk behavior is static, i.e. low risk persons never engage in high-risk behaviors over time. However, the extent of heterogeneity and whether contact structure changes over time for SARS-CoV-2 spread are yet to be quantified through rigorous epidemiological studies. Therefore, cautions need to be made when disease induced immunity thresholds are used for public health policy making.

Recent COVID-19 vaccine trials show that they are highly efficacious in preventing disease (Moderna, 2020, Pfizer, 2020); however, it is still not known how effective they protect from infection and how long the protective immunity lasts. We found that if the duration of immunity is relatively short as suggested in Long et al., 2020, Seow et al., 2020, and similar to the durations of protective immunity against other endemic coronaviruses (Callow et al., 1990, Kissler et al., 2020) or MERS-CoV (Payne et al., 2016), a frequent vaccination schedule once every couple of years to multiple times per year is needed to maintain herd immunity. Furthermore, we found that in addition to the mean duration of vaccine-induced protective immunity, the distribution of the duration is an important factor in determining vaccination frequency. A vaccine that induces a more uniform response in a population is better than a vaccine that induces a heterogeneous response in maintaining population immunity. Studies of the kinetics of antibody dynamics in individuals, such as Antia et al., 2018, Seow et al., 2020, will help making more precise predictions of vaccine schedules.

Overall, our work shows that SARS-CoV-2 has high R0 values and spread very rapidly in the absence of strong control measures across different countries. This implies very high herd immunity thresholds, and thus highly effective vaccines with high levels of population coverage will be needed to prevent sustained transmission. If the protective immunity induced by vaccination is not long lasting, understanding the full distribution of the duration of protective immunity in the population is crucial to determine the frequency of vaccinations.


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