Transmission of an infection requires three conditions:
an infectious individual
a susceptible individual
an effective contact between them
An effective contact is defined as any kind of contact between two individuals such that, if one individual is infectious and the other susceptible, then the first individual infects the second. Whether or not a particular kind of contact will be effective depends on the infectious agent and its route of transmission.
The effective contact rate (denoted β) in a given population for a given infectious disease is measured in effective contacts per unit time. This may be expressed as the total contact rate (the total number of contacts, effective or not, per unit time, denoted ), multiplied by the risk of infection, given contact between an infectious and a susceptible individual. This risk is called the transmission risk and is denoted p. Thus:
The total contact rate, , will generally be greater than the effective contact rate, β, since not all contacts result in infection. That is to say, p can never be greater than 1, since it is effectively the probability of transmission occurring.
This relation formalises the fact that the effective contact rate depends not only on the social patterns of contact in a particular society (γ) but also on the specific types of contact and the pathology of the infectious organism (p). For example, it has been shown that a concurrent sexually transmitted infection can substantially increase the probability (p) of infecting a susceptible with HIV. Therefore, one way to reduce the value of p (and hence lower HIV transmission rates) might be to treat other sexually transmitted infections.
There are a number of difficulties in using this relation. The first is that it is very difficult to measure contact rates because they vary widely between individuals and groups, and within the same group at different times. For sexually transmitted infections, large scale studies of sexual behaviour have been set up to estimate the contact rate.