Bounds for bounded motion around a perturbed fixed point

We consider a dissipative map of the plane with a bounded perturbation term. This perturbation represents e.g. an extra time dependent term, a coupling to another system or noise. The unperturbed map has a spiral attracting fixed point. We derive an analytical/numerical method to determine the effect of the additional term on the phase portrait of the original map, as a function of the δ bound on the perturbation. This method yields a value δ c such that for δδ c the orbits about the attractor are certainly bounded. In that case we obtain a largest region in which all orbits remain bounded and a smallest region in which these bounded orbits are captured after some time (the analogue of 'basin' and 'attractor respectively')

Transient periodic behaviour related to a saddle-node bifurcation

The authors investigate transient periodic orbits of dissipative invertible maps of R2. Such orbits exist just before, in parameter space, a saddle-node pair is formed. They obtain numerically and analytically simple scaling laws for the duration of the transient, and for the region of initial conditions which evolve into transient periodic orbits. An estimate of this region is then obtained by the construction-after extension of the map to C2-of the stable manifolds of the two complex saddles in C2 that bifurcate ino the real saddle-node pai

Recommendations for the prevention of hepatitus A based on a cost-effectiveness analysis

Background. Hepatitis A viral infection poses a substantial risk for travelers from low-endemic countries visiting high-endemic destinations. In this study, the general indications for the optimal prevention of hepatitis A are derived using a cost-effectiveness analysis based on the risk exposure determined by frequency and duration of travel as well as natural immunity. Methods. Three possible hepatitis A prevention strategies are compared to no prophylaxis: active immunization; an initial screening for HAV followed by active immunization of susceptible travelers; and passive immunization with immune globulins. Using a number of baseline assumptions, a scenario for travel from low- to high-endemic countries and an average travel duration and frequency rate, threshold values were obtained comparing active versus passive immunization. Results. The study shows that, for travelers not expected to journey more than twice in a 10-year period, passive immunization is the most cost-effective prophylaxis for travel from both very-low or low-to-high endemic areas. For more frequent travel, vaccination is more cost effective, as well as for journeys of 6-months' duration or longer. As well, pretravel screening before vaccination was shown to be worthwhile, except when the probability of natural immunity is low. Conclusions. As the results indicate, the cost effectiveness of a strategy is related to several considerations: the prices of vaccine and screening tests, travel destinations and endemic conditions, frequency and duration of travel, and natural immunity. A decision-tree-based simulation model is helpful in determining the strategy to emplo

Hepatitis B prevention in Europe: a preliminary economic evaluation

The World Health Organization (WHO) estimates that about 350 million people in the world are carriers of the hepatitis B virus (HBV), 60 million of whom may die from liver cancer and about 45 million from cirrhosis. In the WHO European Region, which has a total population of 839 million inhabitants, the average number of acute hepatitis B cases reported in 1991 was approximately 160 000, giving an incidence of 19 per 100 000 population. This incidence rate varies from 5 per 100 000 in western Europe to 22 per 100 000 in central Europe and 92 per 100 000 in eastern Europe. Because of under-reporting and the fact that two-thirds of infections are asymptomatic, the reported incidence rate considerably underestimates the true incidence of HBV in Europe. For this reason, we may multiply the number of reported cases by a factor of 6 (by 2 for under-reporting and by 3 for the symptomatic/asymptomatic ratio): an estimated 900 000 to 1 000 000 infections of HBV occur in Europe each year. Approximately 90 000 chronic infections will develop from these new cases. The spread of HBV can be controlled by universal infant or adolescent vaccination. A decision-tree-based analytical model was used to assess the clinical and economic impact of these two interventions. The model took into account incidence and prevalence rates of HBV, natural history of infection, compliance and effectiveness of vaccination, and direct and indirect costs. Data were obtained from the literature and from a WHO European survey. The cost-effectiveness ratio amounts to £6443 and £4745 per infection prevented for neonatal and adolescent vaccination, respectively. The results from these calculations show that neither vaccination of neonates or of adolescents is cost-saving. However, the cost-effectiveness - i.e. the cost incurred to prevent an HBV infection is of an acceptable magnitude for both strategies