Dose-Optimal Vaccine Allocation over Multiple Populations

Vaccination is an effective way to prevent an epidemic. It results in immunity for the vaccinated individuals, but it also reduces the infection pressure for unvaccinated people. Thus people may actually escape infection without being vaccinated: the so-called “herd effect.” We analytically study the relation between the herd effect and the vaccination fraction for the seminal SIR compartmental model, which consists of a set of differential equations describing the time course of an epidemic. We prove that the herd effect is in general convex-concave in the vaccination fraction and give precise conditions on the epidemic for the convex part to arise. We derive the significant consequences of these structural insights for allocating a limited vaccine stockpile to multiple non-interacting populations. We identify for each population a unique vaccination fraction that is most efficient per dose of vaccine: our dose-optimal coverage. We characterize the solution of the vaccine allocation problem and we show the crucial importance of the dose-optimal coverage. A single dose of vaccine may be a drop in the ocean, but multiple doses together can save a population. To benefit from this, policy makers should select a subset of populations to which the vaccines are allocated. Focusing on a limited number of populations can make a significant difference, whereas allocating equally to all populations would be substantially less effective

A pharmacoeconomic evaluation of the effects of atorvastatin on early recurrent ischemic events in acute coronary syndromes in Spain

Atorvastatin, Acute coronary syndrome, Cost,

Political participation, diffused governance, and the transformation of democracy : patterns of change

Although democratic governments have introduced a number of institutional reforms in part intended to increase citizens’ political involvement, studies show a continued decline in regular political engagement. This book examines different forms of political participation in democracies, and in what way the delegation of public responsibilities—or, the diffusion of politics—has affected patterns of participation since the 1980s. The book addresses this paradox by directly investigating the impact of institutional changes on citizens’ political participation empirically. It re-analyses patterns of political participation in contemporary democracies, providing an in-depth time series cross-sectional analysis that helps develop a better understanding of how variation in political participation can be explained, both between countries and over time. As such, it develops an institutional theoretical framework which can help to explain levels of participation and shows that, instead of displaying more political apathy, citizens have reallocated or displaced their activities to a broader array of forms of participation.-- Part I: The Changing Democratic System -- 1. Patterns of Change -- 2. The Three Sides of the Coin: Unpacking Political Participation -- 3. Structuring Diffusion: Explaining Levels of Political Participation -- Part II: Patterns of Participation: The Impact of Competence Diffusion -- 4. Participation and Horizontal Diffusion -- 5. Participation and Vertical Diffusion -- 6. Political Participation and Diagonal Diffusion -- Part III: Democracy at the Crossroads? Some Conclusions -- 7. Levels of Political Participation and Multi-Directional Diffusion -- 8. Patterns of Change: Diffused DemocracyPublished version of EUI PhD thesis, 201