Endemicity
In epidemiology, an infection is said to be endemic (from Greek ἐν en "in, within" and δῆμος demos "people") in a population when that infection is maintained in the population without the need for external inputs. For example, chickenpox is endemic (steady state) in the UK, but malaria is not. Every year, there are a few cases of malaria reported in the UK, but these do not lead to sustained transmission in the population due to the lack of a suitable vector (mosquitoes of the genus Anopheles). While it might be common to say that AIDS is "endemic" in Africa, meaning found in an area, this is a use of the word in its etymological not epidemiological form. AIDS cases in Africa are increasing, so the disease is not in an endemic steady state. It is correct to call the spread of AIDS in Africa an epidemic.
For an infection that relies on person-to-person transmission to be endemic, each person who becomes infected with the disease must pass it on to one other person on average. Assuming a completely susceptible population, that means that the basic reproduction number (R0) of the infection must equal 1. In a population with some immune individuals, the basic reproduction number multiplied by the proportion of susceptible individuals in the population (S) must be 1. This takes account of the probability of each individual to whom the disease may be transmitted being susceptible to it, effectively discounting the immune sector of the population. So, for a disease to be in an endemic steady state it is:
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