Reframing Optimal Control Problems for Infectious Disease Management in Low-Income Countries

Optimal control theory can be a useful tool to identify the best strategies for the management of infectious diseases. In most of the applications to disease control with ordinary differential equations, the objective functional to be optimized is formulated in monetary terms as the sum of intervention costs and the cost associated with the burden of disease. We present alternate formulations that express epidemiological outcomes via health metrics and reframe the problem to include features such as budget constraints and epidemiological targets. These alternate formulations are illustrated with a compartmental cholera model. The alternate formulations permit us to better explore the sensitivity of the optimal control solutions to changes in available budget or the desired epidemiological target. We also discuss some limitations of comprehensive cost assessment in epidemiology

Regional patterns of U.S. household carbon emissions

Market-based policies to address fossil fuel-related externalities including climate change typically operate by raising the price of those fuels. Increases in energy prices have important consequences for a typical U.S. household that spent almost $4,000 per year on electricity, fuel oil, natural gas, and gasoline in 2005. A key question for policymakers is how these consequences vary over different regions and subpopulations across the country—especially as adjustment and compensation programs are designed to protect more vulnerable regions. To answer this question, we use non-publicly available data from the U.S. Consumer Expenditure Survey over the period 1984–2000 to estimate long-run geographic variation in household use of electricity, fuel oil, natural gas, and gasoline, as well as the associated incidence of a$10 per ton tax on carbon dioxide (ignoring behavioral response). We find substantial variation: incidence from the tax range from $97 dollars per year per household in New York County, New York to$235 per year per household in Tensas Parish, Louisiana. This variation can be explained by differences in energy use, carbon intensity of electricity generation, and electricity regulation

Connections between Classical and Parametric Network Entropies

This paper explores relationships between classical and parametric measures of graph (or network) complexity. Classical measures are based on vertex decompositions induced by equivalence relations. Parametric measures, on the other hand, are constructed by using information functions to assign probabilities to the vertices. The inequalities established in this paper relating classical and parametric measures lay a foundation for systematic classification of entropy-based measures of graph complexity

Optimal siting, sizing, and enforcement of marine protected areas

The design of protected areas, whether marine or terrestrial, rarely considers how people respond to the imposition of no-take sites with complete or incomplete enforcement. Consequently, these protected areas may fail to achieve their intended goal. We present and solve a spatial bio-economic model in which a manager chooses the optimal location, size, and enforcement level of a marine protected area (MPA). This manager acts as a Stackelberg leader, and her choices consider villagers’ best response to the MPA in a spatial Nash equilibrium of fishing site and effort decisions. Relevant to lower income country settings but general to other settings, we incorporate limited enforcement budgets, distance costs of traveling to fishing sites, and labor allocation to onshore wage opportunities. The optimal MPA varies markedly across alternative manager goals and budget sizes, but always induce changes in villagers’ decisions as a function of distance, dispersal, and wage. We consider MPA managers with ecological conservation goals and with economic goals, and identify the shortcomings of several common manager decision rules, including those focused on: (1) fishery outcomes rather than broader economic goals, (2) fish stocks at MPA sites rather than across the full marinescape, (3) absolute levels rather than additional values, and (4) costless enforcement. Our results demonstrate that such naïve or overly narrow decision rules can lead to inefficient MPA designs that miss economic and conservation opportunities

Spatial resource wars: A two region example

We develop a spatial resource model in continuous time in which two agents strategically exploit a mobile resource in a two-location setup. In order to contrast the overexploitation of the resource (the tragedy of commons) that occurs when the player are free to choose where to fish/hunt/extract/harvest, the regulator can establish a series of spatially structured policies. We compare the three situations in which the regulator: (a) leaves the player free to choose where to harvest; (b) establishes a natural reserve where nobody is allowed to harvest; (c) assigns to each player a specific exclusive location to hunt. We show that when preference parameters dictate a low harvesting intensity, the policies cannot mitigate the overexploitation and in addition they worsen the utilities of the players. Conversely, in a context of harsher harvesting intensity, the intervention can help to safeguard the resource, preventing the extinction and also improving the welfare of both players