Contact Matrices

The various patterns of contacts between individuals, which are necessary for transmission of infection to occur, clearly are not dependent on the presence of a particular infection (although it is true that the presence of infection may lead to changes in patterns of behavior that might result in contacts being made). As prevalence and perhaps intensity or duration of an infection will vary between age groups and between the various subgroups that make up a population, the patterns of contact between these may be important determinants of the dynamics of the infection in the population and the age distribution of infection and hence of the burden of disease. It is therefore advantageous to be able to include a representation of such contact patterns when modeling the transmission dynamics of infection. Although such a representation cannot hope to reproduce the full richness of patterns of contact found in everyday life, nevertheless there are greatly simplified ways of representing such patterns, which nonetheless allow some of the essence of these patterns to be usefully captured. In the com-partmental models described in this chapter, this is typically achieved by the use of a matrix specifying the proportion of contacts made by each group with every other group represented in the model (i.e., contacts which would result in transmission of infection if made with an infectious individual). Typically, for infections such as measles which may be acquired simply through close proximity to a infective case, the contact matrix is presented in the form of a ''Who Acquires Infection from Whom'' (WAIFW) matrix (Anderson and May, 1985; Anderson and Grenfell, 1986; Anderson and May, 1991) in which the individual elements of the matrix represent the probability per unit of time that a susceptible individual in one subgroup (often an age group) may be infected by an infective individual from the same or one of the other subgroups. There is not normally sufficient data to be able to specify the elements of the WAIFW matrix directly, so estimates of the force of infection for each group may be used in combination with estimates of the proportion of the precontrol population in the infective state to estimate the matrix indirectly (there are also strong constraints on the form which the WAIFW matrix may take using this procedure) (Anderson and May, 1991). In the case of sexually transmitted infections (STIs) the contact matrix might simply describe the proportion of its sexual partnerships (or sexual acts) that each subgroup has with each of the other subgroups; then the numbers of partners and/or acts per unit time for individuals in each subgroup together with the probability of transmission per partnership (or per act) are specified as separate parameters (Anderson and May, 1991; Williams and Anderson, 1994).

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