Economic Incentives in the Socially Optimal Management of Infectious Disease: When [Formula: see text] is Not Enough.

Does society benefit from encouraging or discouraging private infectious disease-risk mitigation? Private individuals routinely mitigate infectious disease risks through the adoption of a range of precautions, from vaccination to changes in their contact with others. Such precautions have epidemiological consequences. Private disease-risk mitigation generally reduces both peak prevalence of symptomatic infection and the number of people who fall ill. At the same time, however, it can prolong an epidemic. A reduction in prevalence is socially beneficial. Prolongation of an epidemic is not. We find that for a large class of infectious diseases, private risk mitigation is socially suboptimal-either too low or too high. The social optimum requires either more or less private mitigation. Since private mitigation effort depends on the cost of mitigation and the cost of illness, interventions that change either of these costs may be used to alter mitigation decisions. We model the potential for instruments that affect the cost of illness to yield net social benefits. We find that where a disease is not very infectious or the duration of illness is short, it may be socially optimal to promote private mitigation effort by increasing the cost of illness. By contrast, where a disease is highly infectious or long lasting, it may be optimal to discourage private mitigation by reducing the cost of disease. Society would prefer a shorter, more intense, epidemic to a longer, less intense epidemic. There is, however, a region in parameter space where the relationship is more complicated. For moderately infectious diseases with medium infectious periods, the social optimum depends on interactions between prevalence and duration. Basic reproduction numbers are not sufficient to predict the social optimum.

Limiting Similarity, Species Packing, and System Stability for Hierarchical Competition-Colonization Models.

Hierarchical competition-colonization models have been used to explain limiting similarities among species, successional dynamics, and species loss under habitat destruction. This class of models assumes that there is an inverse relationship between competitive ability and colonization ability and that competitively superior species exclude competitively inferior species when both occupy the same site. This hierarchical model of performance trade-offs, however, exhibits some unusual behaviors in the high-diversity limit, including infinitesimally close species packing, pathologically slow dynamics, and fundamentally important regularities in trait-abundance relationships. In particular, under the condition of constant mortality across species, a 3/2-power-law relationship emerges between abundance and fecundity under infinite packing (abundance of a species with fecundity f is inversely proportional to f to the 3/2 power). In this article, we explore the high-diversity limit of the hierarchical competition-colonization model, with particular emphasis on patterns of species packing, species-abundance relationships, and system stability. Because of the potential for pathologically slow dynamics following perturbations and infinitesimally close species packing in the high-diversity limit for this class of models, the models may need to be modified to include more realistic mechanisms governing the extent and timing of interspecific competitive exclusion in order to effectively capture the structure and dynamics of real-world ecosystems.

Mutualism and competition between plants and decomposers: implications for nutrient allocation in ecosystems.

By examining the consequences of simultaneous mutualism and competition between plants and decomposers, we show that testable predictions about nutrient allocation in ecosystems follow from the assumption that decomposers allocate for their own growth the fraction of mineralized nutrient that maximizes their population biomass, leaving the remainder available for plant uptake. Available data for a wide variety of ecosystems are nearly all consistent with the predicted quantitative relationships among nitrogen flow rates and nitrogen fractions in plants, decomposers, and nonliving organic matter. Our predictions are robust against changes in the detailed structure of the nutrient-cycle models we use for our derivations.