BACKGROUND: Strong regional heterogeneity and generally sub-optimal rates of measles vaccination in Italy have, to date, hampered attainment of WHO targets for measles elimination, and have generated the need for the new Italian National Measles Elimination Plan. Crucial to success of the plan is the identification of intervention priorities based upon a clear picture of the regional epidemiology of measles derived from the use of data to estimate basic parameters. Previous estimates of measles force of infection for Italy have appeared anomalously low. It has been argued elsewhere that this results from Italian selective under-reporting by age of cases and that the true measles force of infection in Italy is probably similar to that of other European countries. A deeper examination of the evidence for this conjecture is undertaken in the present paper. METHODS: Using monthly regional case notifications data from 1949 to the start of vaccination in 1976 and notifications by age from 1971-76, summary equilibrium parameters (force of infection (FOI), basic reproductive ratio (R0) and critical vaccination coverage (pc)) are calculated for each region and for each of 5 plausible contact patterns. An analysis of the spectra of incidence profiles is also carried out. Finally a transmission dynamics model is employed to explore the correspondence between projections using different estimates of force of infection and data on seroprevalence in Italy. RESULTS: FOI estimates are lower than comparable European FOIs and there is substantial regional heterogeneity in basic reproductive ratios; certain patterns of contact matrices are demonstrated to be unfeasible. Most regions show evidence of 3-year epidemic cycles or longer, and compared with England & Wales there appears to be little synchronisation between regions. Modelling results suggest that the lower FOI estimated from corrected aggregate national data matches serological data more closely than that estimated from typical European data. CONCLUSION: Results suggest forces of infection in Italy, though everywhere remaining below the typical European level, are historically higher in the South where currently vaccination coverage is lowest. There appears to be little evidence to support the suggestion that a higher true force of infection is masked by age bias in reporting.

In this paper we consider the estimation of some stochastic differential equation models by an indirect estimation method proposed by Gourieroux, Monfort and Renault (1993) using discrete data. The performance of this method is analysed via Monte Carlo experiments. In particular we examine the Vasicek and the Cox, Ingersoll and Ross models used in financial economics and a system of three stochastic differential equations proposed by P.C.B. Phillips in 1972. These results show the ability of indirect estimation to remove the bias resulting from the discretisation of the continuous model.

The problem of computing the maximum likelihood estimate of the parameters of a speci®c class of stochastic differential equation (SDE) models with linear drift whose sample paths are observed at discrete time points is considered. This estimate is obtained as in Cleur and Manfredi (1999) by discretizing the explicit expressions for the estimates which maximize the likelihood function in continuous time, by discretizing the likelihood function through a quadrature approximation before maximizing it, and by maximizing the likelihood function of the Euler scheme approximation to the underlying continuous process. Simulation results indicate that, for the constellation of parameter values considered, all three approaches lead to very similar results.

No abstract

No abstract