Population-dynamics models and a sequential test in the analysis of the influence of household setting on the spread of Variola minor

Abstract

The Wald sequential probability ratio test was used to analyze the effects of household setting upon dates of onset of Variola minor (alastrim) during an epidemic occurring in Braganga Paulista County, Brazil, in 1956. Four population-dynamics models were used, depending upon whether the probability of occurrence of new cases was assumed to be (a) a function of the number of infectives (Simple Birth); (b) a function of the number of remaining uninfected susceptibles (Simple Death); (c) a function of both the number of infectives and a constant removal rate due to isolation, recovery or death (Simple Birth-Death) and, (d) a function of a “parameter of contagiousness” so as to increase with increasing numbers of infectives and decrease with time since the last infective (Polyá). The last two processes gave larger numbers of significant differences related to environment. These differences were consistent with generally accepted knowledge and with notions intuitively derived from the empirical findings. Environment was thus often found to differentiate subsequent cases (seemingly resulting from within-household spread) while only rarely affecting the rate of occurrence of cases introducing the disease into households (seemingly resulting from between-households spread). Rural and semi-rural settings showed greater similarity than either did with the urban environment.