[Epidemiology of hepatitis A in Sardinia: mathematical model]

The prevalence of antibodies to hepatitis A in South-Sardinia was determined in samples of students and workers. In 1987 sera were collected from the children who attended kindergarten and elementary schools, in 1988 from students 13-20 years old (high schools) and from a group of workers who went to the public health office to ask for a certificate of good health. As far as the workers are concerned, the force of infection can be taken as a constant. In childhood, on the contrary, our findings are suggestive for a different immunization model. In this research work the prevalence observed in the population is analyzed using a mathematical model. Our model is based on the assumption that the force of infection increases linearly with age. The estimated fraction of susceptibles to hepatitis A is denoted by Y (X). The parameter h (X) represents the force of infection, the per capita rate at which susceptible population acquires infection. We assume that susceptibility may be lost only by natural infection and that permanent immunity results from first infection. So the fraction of susceptible population is gamma = exp (- x o integral of h (chi) d chi) if the force of infection increases linearly with age h (X) = ax + b then Y = exp (aX2 + bX + c) We can write In Y = y We obtain y = aX2 + bX + c Goodness of fit has been tested using the coefficient of determination R2. The number of cases in the group of age X - X + 1 can be estimated, for 10000 inhabitants, as (Y (X) - Y(X + 1) * 10000) Our findings are suggestive for a linear increasing of the force of infection with the group of age (R2 = 0.974). This could result from an age-dependent force of infection presumably as a consequence of age-related changes in behavioural patterns. Another explication could be a time-dependent force of infection according to improvements in socioeconomic and hygienic conditions. There is clear need for further research to separate the variations attributable to age from those attributable to time. Case notifications records could be very useful, but these data are notoriously unreliable.