Basic reproduction number

In epidemiology, the basic reproduction number, or basic reproductive number (sometimes called basic reproduction ratio or basic reproductive rate), denoted (pronounced R nought or R zero), of an infection is the expected number of cases directly generated by one case in a population where all individuals are susceptible to infection. The definition assumes that no other individuals are infected or immunized (naturally or through vaccination). Some definitions, such as that of the Australian Department of Health, add the absence of "any deliberate intervention in disease transmission". The basic reproduction number is not necessarily the same as the effective reproduction number (usually written [t for time], sometimes ), which is the number of cases generated in the current state of a population, which does not have to be the uninfected state. is a dimensionless number (persons infected per person infecting) and not a time rate, which would have units of time−1, or units of time like doubling time. is not a biological constant for a pathogen as it is also affected by other factors such as environmental conditions and the behaviour of the infected population. values are usually estimated from mathematical models, and the estimated values are dependent on the model used and values of other parameters. Thus values given in the literature only make sense in the given context and it is recommended not to use obsolete values or compare values based on different models. does not by itself give an estimate of how fast an infection spreads in the population. The most important uses of are determining if an emerging infectious disease can spread in a population and determining what proportion of the population should be immunized through vaccination to eradicate a disease. In commonly used infection models, when the infection will be able to start spreading in a population, but not if . Generally, the larger the value of , the harder it is to control the epidemic.