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

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

Het Schelde-estuarium als filter: een bioreactor van stofstromen

The Scheldt estuary is exposed to large loads of carbon and nutrients. This leads to a eutrophication problem characterized by reduced oxygen concentrations and a huge efflux of CO2. In the coastal waters a degradation of the foodchain is noted caused by excessive nutrient supply. The capacity of the estuary to polish the water is important but can not cope with the vast scale of the immissions. Restoration and development of tidal wetlands can contribute in several ways to restore the water quality. Increase of water treatment is expected to have positive ecological results. Nevertheless, restoration of the oxygen conditions might counteract some purifying processes