R-naught: AKA The basic reproduction rate or R-zero (Ro). Essentially, the general contagiousness of an organism in “naive” population all things considered.

R-naught is the average number of cases that each infected case will themselves directly infect over time assuming there is no natural or vaccine mediated immunity in the population (and in some definitions assuming the absence of any mitigating interventions such as social distancing, hand washing campaigns, etc.). It is used to help understand what percentage of the population needs to be vaccinated to achieve herd immunity. Several features of R-naught merit attention:

  • R-naught is a function of the the biology of the disease and features of the population :
    • Biology of the organism and its disease:
      • Duration of transmissability, vector of transmission, viability of the organism, inoculation dose, and
    • Features of the population:
      • Demographics of the community, social norms and habits, living structures, and the health status of the community.
  • R-naught is a dimensionless statistic (in contrast for example to the doubling rate) and it does not independently tell us how fast a disease will spread in a population.
  • R-naught is specific to a community.
  • If you are following closely you will have understood that R-naught is not influenced by vaccination, but it can be influenced by behavioural public health interventions.

Ro should NOT be confused with R, the “effective reproduction number” (the average number of new cases that are expected to arise from an infected case in the current situation).  In basic models, the math of Ro is simple. Ro > 1 means that the disease will be able to start spreading in a population. As point of reference here are  estimated values for known infections:

c. difficile1.3
Hanta Virus1.3
Meningococcal Meningitis1.3
Marburg Virus1.6
Typhoid Fever2.8
Spanish Flu (1918)3
Hepatitis B4
Common cold (Rhinovirus)6


      • Influenza ———- Ro
      • MERS ————- Ro
      • SARS ————- Ro
      • COVID-19 ——– Ro
      • Measles ———- Ro

Ro is used to estimate the percent of effective immunity it takes to provide herd immunity, by the formula: Neutralizing immunity = 1-1/Ro