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Using the ALIENOR transformation avoids the problem of determining the first and second derivatives of the objective functional f when using the multidimensional bissection method. Knowledge of the Lipschitzian constant C is generally sufficient for using this method, and therefore for determining the global maximum of f defined on a compact set.

Background: The epidemiological pattern of hepatitis A infection has shown dynamic changes in many parts of the world due to improved socioeconomic conditions and the accumulation of seronegative subjects, which leads to possible outbreaks and increased morbidity rate. In Tunisia, the epidemiological status of hepatits A virus is currently unknown. However, over the past years higher numbers of symptomatic hepatitis A virus infection in school attendants and several outbreaks were reported to the Ministry of Health, especially from regions with the lowest socioeconomic levels in the country. The aim of this study was to investigate the current seroprevalence of hepatitis A virus antibodies in central-west Tunisia and assess the impact of hepatitis A virus vaccination on hepatitis A epidemiology. Methods: Serum samples from 1379 individuals, aged 5-75 years, were screened for hepatitis A virus antibodies. Adjusted seroprevalence, incidence and force of infection parameters were estimated by a linear age structured SEIR (Susceptible-Exposed-Infectious-Recovered) compartmental model. A vaccine model was then constructed to assess the impact on hepatitis A virus epidemiology of 3 scenarios of vaccination strategies: one dose at 12-months of age, one dose at 6-years and one dose at 12-months and another at 6-years of age during 6 years. Results: A rapid increase in anti-hepatitis A virus seroprevalence was noted during infancy and adolescence: 47% of subjects under 10-years-old are infected; the prevalence increases to 77% at 15-years and reaches 97% in subjects aged 30-years. The force of infection is highest between 10 and 30-years of age and the incidence declines with increasing age. The vaccine model showed that the 3-scenarios lead to a significant reduction of the fraction of susceptibles. The two doses scenario gives the best results. Single-dose vaccination at 6-years of age provides more rapid decrease of disease burden in school-aged children, as compared to single-dose vaccination at 12-months, but keeps with a non-negligible fraction of susceptibles among children < 6-years.

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Suggests a unidimensional model for determining the analytical solution of the diffusion of antibodies in tumours. By using the Alienor technique, identifies the parameters characterizing this diffusion and calculates the interval between steps.