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# Susceptible

In epidemiology a susceptible individual (sometimes known simply as a susceptible) is a member of a population who is at risk of becoming infected by a disease, if they are exposed to the infectious agent.

Susceptibles have been exposed to neither the wild strain of the disease nor a vaccination against it, and thus have not developed immunity. Those individuals who have antibodies against an antigen associated with a particular infectious disease will not be susceptible, even if they did not produce the antibody themselves (for example, infants younger than six months who still have maternal antibodies passed through the placenta and from the colostrum, and adults who have had a recent injection of antibodies). However, these individuals soon return to the susceptible state as the antibodies are broken down.

Some individuals may have a natural resistance to a particular infectious disease. However, except in some special cases, these individuals make up such a small proportion of the total population that they can be ignored for the purposes of modelling an epidemic.

The proportion of the population who are susceptible to a particular disease is denoted S. Due to the problems mentioned above, it is difficult to know this parameter for a given population. However, in a population with a rectangular population distribution (such as that of a developed country), it may be estimated by:

${S} = \frac {A} {L}$

Where A is the average age at which the disease is contracted and L is the average life expectancy of the population. To understand the rationale behind this relation, think of A as the length of time spent in the susceptible group (assuming an individual is susceptible before contracting the disease and immune afterwards) and L as the total length of time spent in the population. It thus follows that the proportion of time spent as a susceptible is A/L and, in a population with a rectangular distribution, the proportion of an individual's life spent in one group is representative of the proportion of the population in that group.

The advantage of estimating S in this way is that both the average age of infection and average life expectancy will be well documented, and thus the other parameters needed to calculate S will be easily at hand.

The parameter S is important in the mathematical modelling of epidemics.