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 one. In a population with some
immune individuals, the basic reproduction number multiplied by the proportion of
susceptible individuals in the population (
S) must be one. 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 or
endemic equilibrium, it holds that : R_0 \times S = 1 In this way, the infection neither dies out, nor does the number of infected people increase
exponentially. An infection that starts as an epidemic will eventually either die out (with the possibility of it resurging in a theoretically predictable cyclical manner) or reach the endemic steady state, depending on a number of factors, including the
virulence of the disease and its
mode of transmission. If a disease is in an endemic steady state in a population, the relation above allows the
basic reproduction number (R0) of a particular infection to be estimated. This in turn can be fed into a
mathematical model for the epidemic. Based on the reproduction number, we can define the epidemic waves, such as the first wave, second wave, etc. for COVID-19 in different regions and countries. == Misuse ==