Optimal disease management : a dairy herd application
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Animal disease programs usually recommend high applications of drugs and pesticides to control or eliminate the disease without regard to economics. This is particularly true in the case of infectious animal disease because of the dynamics and uncertainty associated with its spread. On the assumption that these programs arc inefficient from the decision maker's perspective, a theoretical model of this problem was developed. The model considers both the problems of disease dynamics and decision making under uncertainty with regard to disease prevalence and the impacts of disease on production. Theoretical results suggested that total elimination of the disease may not be optimal and that control strategies based on known infection status or thresholds may be more efficient than total application strategies. Comparative dynamics showed that an increase in the intertemporal discount rate would increase the threshold level at every point on the time path to the new steady state. It was also hypothesized that an increase in risk aversion would decrease the steady state threshold. A stochastic simulation model of paratuberculosis in a Wisconsin dairy herd was modified to permit flexible control strategies based on threshold levels. Eleven strategies were evaluated including: a 100 percent vaccination strategy, vaccination above specified threshold levels, vaccination above and cull below threshold levels, a 100 percent cull strategy and good sanitary conditions only. Stochastic dominance techniques were applied to distributions of net present value of profit. This assumes that expected value of net present value of the outcome is the appropriate maximization criterion, which requires restrictive assumptions on decision maker utility functions and/or preferences concerning temporal flow of outcomes. For comparison, the net present value of a negative exponential utility function was calculated at comparative levels of risk aversion. Results indicated that, under conditions specified for the simulation model, total elimination of the disease is optimal and occurred in all but one strategy, good sanitary conditions only. The 100 percent vaccination strategy is optimal for all individuals ranging from moderately strong risk loving to extreme risk averse. Extreme risk loving individuals were found to have several threshold based strategies as part of their efficiency set. There was supporting evidence that increases in risk led to lower threshold levels and that increases in the discount rate led to higher threshold levels. Comparisons between the two approaches to temporal resolution of outcomes indicated differences. The net present value of expected utility gave the 100 percent cull strategy as the optimal strategy for moderately risk adverse individuals. This contrasts with the 100 percent vaccination strategy being optimal for the alternative approach. This finding points out the danger of relying on distributions of net present values of outcomes for temporal decision analysis. Advances in multiattribute stochastic dominance may alleviate these problems.
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