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What is R “nought” (R0)?

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Last Updated: 02.01.2020

Many factors contribute to how disease is spread including (but not limited to): the type of pathogenic microbe; the lifespan of the microbe; any special features of the microbe; the disease vector (and its location, movement, lifespan, lifestyle characteristics/habits); the location/weather/natural barriers/migration patterns; the age/health/nutrition profile/lifestyle/habits of the infected person and his/her location plus the number of people that the infected person may encounter daily; the people in daily contact with the infected person and these people’s age/health/nutrition profile/lifestyle etc.

These details are elements of the epidemiologic triad (agent, host, and environmental factors) (Delamater, Street, Leslie, Yang, & Jacobsen, 2019). In epidemiology, R0 is used to estimate how infectious a pathogen might be (especially novel pathogens and potential outbreaks).

R “nought” or R0 is the basic reproduction number is defined as “the average number of secondary infections generated by the first infectious individual in a population of completely susceptible individuals” (CIDD, 2014a; CIDD, 2014b).

For example, consider person0 who is infected. How long has that person0 been infected? The longer person0 has been infected, the more opportunity there is for person0 to be in contact with more people and potentially infect them. The length of infection (L) is a variable that can increase the value of R0 (CIDD, 2014a; Cintrón-Arias, 2015).

Susceptible hosts (S) are (in this case we are talking about) other people who can potentially catch the disease from person0 (CIDD, 2014a; Cintrón-Arias, 2015 ). If person0 knows a lot of people and is in contact with a lot of people, then the number of susceptible hosts (S) is larger–increase the number of potentially infected people (R0 increases). Also, consider where person0 is living. If person0 is living in New York City where the population density is very high, S can also increase. This may continue on exponentially (CIDD, 2014a; CIDD, 2014b).

R0 also depends on transmissability–how transmissable is a pathogen. What affects transmissability? The properties of the pathogen and the population being studied affect transmissability (B, “beta”). The rate of potentially transmissable contacts (PT) and the likelihood of a successful transmission (ST, the infected person gets sick) are factors in T (CIDDa, 2014).

https://youtu.be/ju26rvzfFg4

ST depends on the characteristics of the pathogen. Some pathogens are very hardy and prolific. For example, you can catch the pathogen just by being in the same room as the sick person. Some pathogens are very fragile and “finicky” making them more difficult to be successfully transmitted–they have many more environmental requirements in order for them to be viable.

Potentially transmissable contacts (PT) is dependent on the characteristics of the population. More susceptible people include those who are very young/elderly, people lacking good nutrition, people who already have other health problems, etc.

R0 is a function of S, L, and B. R0 may be a single value or a low-to-high range. Remember that R0 is a “best guess” for the current situation–it is not definitive. In the case of a novel pathogen, R0 must be modeled off of knowledge of past outbreaks with known pathogens. Complex math, artificial intelligence, dynamic computation, and scientists from many different fields contribute to such work.

If R0>1, then the outbreak is likely to continue; if R0<1, then the outbreak has a better potential for being contained (Delamater et al. 2019). Anticipated outbreak/epidemic size is commonly based on R0 as is the estimation of the number of people needing to be vaccinated (Delamater et al., 2019).

Using available data for 2019-nCoV through January 21st, 2020, Read, Bridgen, Cummings, Ho, and Jacobsen (2019) estimated R0 (model based on human-human transmission, omitting zoonotic transmission) to be 3.8 (95% confidence interval, 3.6 and 4.0) implicating that 72-75% of transmissions must be prevented/controlled in order to stop the increase. Read et al. (2019) also estimated that only 5.1% (95% confidence interval, 4.8-5.5) of the infections in Wuhan have actually been identified/confirmed. It was very likely that the information and statistics released to the media (especially from the Chinese government) were under-reported. Predicted numbers were closer to 191,529 infections by February 4th, 2020 (Read et al., 2019). From rough estimates, R0 for 2019-nCoV are significantly greater than the R0 for MERS-CoV, but closer to the R0 for SARS (Read et al., 2019).

Using Virus Host Prediction (VHP), Zhu et al. (2020) found the infectivity pattern of 2019-nCoV to be more similar to Bat SARS-like coronavirus and mink coronavirus. The Huanan seafood and wet market included sales of produce, mean, and live animals crammed together in stalls (Woodward, 2020; Zhu et al., 2020).

References

Center for Infectious Disease Dynamics (CIDD). (2014a, March 19). Week 1 Video 5: Reproductive Number [Video]. https://youtu.be/ju26rvzfFg4

Center for Infectious Disease Dynamics (CIDD). (2014b, March 19). Week 1 Video 6: Epidemic Curve [Video]. https://youtu.be/sSLfrSSmJZM

Cintrón-Arias, A. (2015, November 4). East Tennessee State University MATH 5880 Basic reproductive number [Video]. https://youtu.be/ItW-Q6Npapo

Delamater, P. L., Street, E. J., Leslie, T. F., Yang, Y. T., & Jacobsen, K. H. (2019). Complexity of the basic reproduction number (R0). Emerging infectious diseases25(1).

Read, J. M., Bridgen, J. R., Cummings, D. A., Ho, A., & Jewell, C. P. (2020). Novel coronavirus 2019-nCoV: early estimation of epidemiological parameters and epidemic predictions. medRxiv.

Woodward, A. (2020, January 31). The outbreaks of both the Wuhan coronavirus and SARS likely started in Chinese wet markets. Business Insider. https://www.businessinsider.com/wuhan-coronavirus-chinese-wet-market-photos-2020-1

Zhu, H., Guo, Q., Li, M., Wang, C., Fang, Z., Wang, P., … & Xiao, Y. (2020). Host and infectivity prediction of Wuhan 2019 novel coronavirus using deep learning algorithm. bioRxiv.