Balancing the benefits of vaccination: An envy-free strategy.

The Covid-19 pandemic revealed the difficulties of vaccinating a population under the circumstances marked by urgency and limited availability of doses while balancing benefits associated with distinct guidelines satisfying specific ethical criteria. We offer a vaccination strategy that may be useful in this regard. It relies on the mathematical concept of envy-freeness. We consider finding balance by allocating the resource among individuals that seem heterogeneous concerning the direct and indirect benefits of vaccination, depending on age. The proposed strategy adapts a constructive approach in the literature based on Sperner's Lemma to point out an approximate division of doses guaranteeing that both benefits are optimized each time a batch becomes available. Applications using data about population age distributions from diverse countries suggest that, among other features, this strategy maintains the desired balance, throughout the entire vaccination period. We discuss complementary aspects of the method in the context of epidemiological models of age-stratified Susceptible - Infected - Recovered (SIR) type.

An integrated model to study varietal diversity in traditional agroecosystems.

Agricultural diversity is one of the bases of traditional agroecosystems, having great environmental and cultural importance. The current loss of agricultural diversity is causing serious concern, mainly because of its essential role in supporting global and local food security. Stopping this loss requires a better understanding of how diversity is managed locally and what mechanisms sustain agricultural diversity. Here we propose a generalist agent-based model that couples biological, cultural, and social dynamics to obtain varietal diversity as an emergent phenomenon at the community level. With a mechanistic approach, we explore how four of the model dynamics can shape systems diversity. To validate the model, we performed a bibliographic review on Manihot esculenta and Zea mays case studies. The model yielded compatible results for manioc and maize varietal richness at both community and household levels.