The incidence (total yearly number of new cases or yearly proportion of the population newly infected) and prevalence of an infection (proportion of the population with current infection) in a population are basic and essential epidemiological measures, and are in principle directly observable or deducible, given an adequate surveillance system, clear case definition, and either unambiguous clinical symptoms or suitable laboratory techniques for confirmation. However, incidence and prevalence cannot be used directly as inputs to a model because these measures are a reflection, among other things, of both the capacity of the infectious agent to spread and also the distribution of prior immunity in the population. What is needed is a measure of the intrinsic ability of the infectious agent to spread from an infected individual to a susceptible individual in the population. The force of infection (FOI, often assigned the Greek letter lambda, A) is the measure that is needed and plays an integral role in the operation of transmission dynamic models. This measure corresponds to the yearly incidence of infection per capita among those individuals who are susceptible to infection, that is, those who are not immune as a result of past infection, the presence of maternal antibody, or effective immunization, or those who are currently infected with the same infectious agent (it will be seen that there are parallels here with R0, the basic reproductive number; see Anderson and May (1991) for a detailed exposition of the relationship between the two). In fact the FOI is a composite of (a) the rate of contacts with other individuals in the population, whether infectious or not; (b) the risk of infection actually being transmitted to another individual given a suitable contact; and (c) the proportion of contacts who are in fact infectious. Depending on the complexity of the model, many simplifying assumptions need to be made if these components of the FOI are to be measured. However, it is also possible for the FOI to be inferred from serological data (prior to introduction of any vaccination) if infection results in long-lasting immunity to further infection and case mortality is relatively small (Farrington, 1990). An additional requirement for this approach is that the infection, to a rough approximation, can be considered to be more or less at equilibrium in the population over the longer term so that the distribution of immunity by age does not change significantly over time. Such stability in the age profile of immunity over time means that measurement at a given time (i.e., cross-sectional measurement) of the age distribution of exposure to infection in a population (i.e., the proportion at each age with the appropriate antibody) may be taken to correspond to a longitudinal measurement over time of exposure to infection of any birth cohort of the population. This cumulative risk can be analyzed in the same way as other cumulative risks by using survival analysis (Farrington, 1990) and making the assumption that everyone entering the population at birth is either susceptible to infection or becomes so following the loss of maternal antibody. The ''failure rate'' resulting from this analysis is the FOI which may be either independent of age or, if the data is sufficiently detailed to warrant it, age-dependent. An alternative to estimation of the FOI in such a population is to make use of case notifications, but the potential weakness of this latter approach lies in the common problem of failures and biases intrinsic to reporting systems; the use of sentinel surveys is likely to prove the more reliable approach. If an infection is newly introduced into a previously unexposed population, which therefore has no immunity, a useful estimate of the FOI can also be derived from R0, which in turn can be estimated from the time taken for the number of cases of the newly introduced infection to double (Anderson et al., 1986; Anderson and May, 1991). When there are no long-lasting markers of infection, mortality is high, infection is not at equilibrium, or there are substantial heterogeneities in patterns of infection in different subgroups of the population, this last method is particularly useful for estimating the FOI. The case of HIV/ AIDS is a notable example where this latter technique has been used in the initial stages of an epidemic (Anderson et al., 1986).
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