2, however this proportion exceeds the population size. Assume the rectangular stationary age distribution and let also the ages of infection have the same distribution for each birth year. Let the average age of infection be A, for instance when individuals younger than A are susceptible and those older than A are immune (or infectious). Then it can be shown by an easy argument that the proportion of the population that is susceptible is given by: We reiterate that L is the age at which in this model every individual is assumed to die. But the mathematical definition of the endemic steady state can be rearranged to give: Therefore, due to the transitive property: This provides a simple way to estimate the parameter R0 using easily available data. For a population with an exponential age distribution, This allows for the basic reproduction number of a disease given A and L in either type of population distribution. Compartmental models in epidemiology Compartmental models are formulated as Markov chains. A classic compartmental model in epidemiology is the SIR model, which may be used as a simple model for modelling epidemics. Multiple other types of compartmental models are also employed. The SIR model In 1927, W. O. Kermack and A. G. McKendrick created a model in which they considered a fixed population with only three compartments: susceptible, ; infected, ; and recovered, . The compartments used for this model consist of three classes: is used to represent the individuals not yet infected with the disease at time t, or those susceptible to the disease of the population. denotes the individuals of the population who have been infected with the disease and are capable of spreading the disease to those in the susceptible category. is the compartment used for the individuals of the population who have been infected and then removed from the disease, either due to immunization or due to death. Those in this category are not able to be infected again or to transmit the infection to others. Other compartmental models There are many modifications of the SIR model, including those that include births and deaths, where upon recovery there is no immunity (SIS model), where immunity lasts only for a short period of time (SIRS), where there is a latent period of the disease where the person is not infectious (SEIS and SEIR), and where infants can be born with immunity