In epidemiology, the basic reproduction number of an infection is the mean number of secondary cases a typical single infected case will cause in a population with no immunity to the disease in the absence of interventions to control the infection. It is often denoted R0 . EPIDEMIOLOGY is the study of the distribution and determinants of disease in human populations (Rothman and Greenland), and the application of this study to control of health problems (Last 2001). ... An infection is the detrimental colonization of a host organism by a foreign species. ... In a medical sense, immunity is a state of having sufficient biological defenses to avoid infection, disease, or other unwanted biological invasion. ...
When
R0 < 1
the infection will die out with certainty. But if
R0 > 1
there is some possibility of a major epidemic. An epidemic is a disease that appears as new cases in the population in a period of time at a rate (the number of new cases in the population during a specified period of time is called the incidence rate) that substantially exceeds what is expected, based on recent experence. ...
If
R0 = 1,
then the infection will become endemic in the population. In epidemiology, an infection is said to be endemic in a population when that infection is maintained in the population without the need for external inputs. ...
Generally, the larger the value of R0, the harder it is to control the epidemic. In particular, the proportion of the population that need to be vaccinated to provide herd immunity and prevent sustained spread of the infection is given by 1-1/R0. The effectiveness of a vaccine depends, amongst other things, on the percentage of the population which has received it and is still within the period of protection offered by that vaccine. ...
Values of R0 of some well-known infectious diseases:
The distribution of A, the total number of infected persons excluding those infected contacts who were vaccinated on time to prevent disease, and B, the time to extinction for 500 simulation runs with the baseline intervention parameter values and a basicreproductionnumber of 5.23.
For a basicreproductionnumber of 10.46 and an increase of the vaccination coverage in the casual contact ring to 80% in C, the distribution of the total number of infected persons, and in D, the distribution of the time to extinction is shown for 500 simulation runs.
The total number of infected persons (excluding successfully vaccinated infected contacts) depends on A, the number of index cases starting the epidemic, and B, the day of the infectious period after which the diagnosis of the first case occurs.
This article uses some basic assumptions and some simple mathematics to find parameters for various infectious diseases and to use those parameters to make useful calculations about the effects of a mass vaccination programme.
S = the proportion of the population (given as a decimal between 0 and 1) who are susceptible to the disease (that is, not immune).
Notice that this relation means that for a disease to be in the endemic steady state, the higher the basicreproductionnumber, the lower the proportion of the population susceptible must be, and vice versa; a mathematical basis for a result that might have been intuitively obvious.
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