On estimating the contagiousness of a disease transmitted from person to person

Abstract A discrete-time model and a continuous-time model, each allowing for two types of susceptibles, are constructed for studying the spread of an infectious disease. The estimation of four parameters is considered for the purpose of assessing the potential (measure of opportunity) that an individual has for provoking the disease in a given susceptible from the same, or from a different, household when the susceptible was, or was not, previously vaccinated. In order to avoid generalities and to support the reasonableness of the basic assumptions, the approach is presented with continuing reference to a detailed data set for an epidemic of variola minor (Brazil, 1956). The empirical application indicated that the within-household and between-households transmission rates differ by a factor of the order of 10 5 for each type of susceptible, thus lending support to the postulate that a contagious disease epidemic effectively consists of the summation of smaller, almost independent outbreaks (occuring, in this case, in the households). In the study epidemic, previous vaccination seemed to reduce the between-households transmission rate much more than the within-household transmission rate. Moreover, on average, the chance that a previously vaccinated susceptable acquires variola minor from an infected person of the same household is about one-fifth of the corresponding chance of an unvaccinated susceptible.