The Economics of Managing Wildlife Disease

The spread of infectious disease among and between wild and domesticated animals has become a major problem worldwide. Upon analyzing the dynamics of wildlife growth and infection when the diseased animals cannot be identified separately from healthy wildlife prior to the kill, we find that harvest-based strategies alone have no impact on disease transmission. Other controls that directly influence disease transmission and/or mortality are required. Next, we analyze the socially optimal management of infectious wildlife. The model is applied to the problem of bovine tuberculosis among Michigan white-tailed deer, with non-selective harvests and supplemental feeding being the control variables. Using a two-state linear control model, we find a two-dimensional singular path is optimal (as opposed to a more conventional bang-bang solution) as part of a cycle that results in the disease remaining endemic in the wildlife. This result follows from non-selective harvesting and intermittent wildlife productivity gains from supplemental feeding.

Bovine Tuberculosis in Swedish Farmed Deer: Detection and Control of the Disease

Bovine tuberculosis (BTB) was introduced into Swedish farmed deer herds in 1987. Epidemiological investigations showed that 10 deer herds had become infected (July 1994) and a common source of infection, a consignment of 168 imported farmed fallow deer, was identified (I). As trace-back of all imported and in-contact deer was not possible, a control program, based on tuberculin testing, was implemented in July 1994. As Sweden has been free from BTB since 1958, few practicing veterinarians had experience in tuberculin testing. In this test, result relies on the skill, experience and conscientiousness of the testing veterinarian. Deficiencies in performing the test may adversely affect the test results and thereby compromise a control program. Quality indicators may identify possible deficiencies in testing procedures. For that purpose, reference values for measured skin fold thickness (prior to injection of the tuberculin) were established (II) suggested to be used mainly by less experienced veterinarians to identify unexpected measurements. Furthermore, the within-veterinarian variation of the measured skin fold thickness was estimated by fitting general linear models to data (skin fold measurements) (III). The mean square error was used as an estimator of the within-veterinarian variation. Using this method, four (6%) veterinarians were considered to have unexpectedly large variation in measurements. In certain large extensive deer farms, where mustering of all animals was difficult, meat inspection was suggested as an alternative to tuberculin testing. The efficiency of such a control was estimated in paper IV and V. A Reed Frost model was fitted to data from seven BTB-infected deer herds and the spread of infection was estimated (< 0.6 effective contacts per deer and year) (IV). These results were used to model the efficiency of meat inspection in an average extensive Swedish deer herd. Given a 20% annual slaughter and meat inspection, the model predicted that BTB would be either detected or eliminated in most herds (90%) 15 years after introduction of one infected deer. In 2003, an alternative control for BTB in extensive Swedish deer herds, based on the results of paper V, was implemented.

Applications of Linear Programming to Coding Theory

Maximum-likelihood decoding is often the optimal decoding rule one can use, but it is very costly to implement in a general setting. Much effort has therefore been dedicated to find efficient decoding algorithms that either achieve or approximate the error-correcting performance of the maximum-likelihood decoder. This dissertation examines two approaches to this problem. In 2003 Feldman and his collaborators defined the linear programming decoder, which operates by solving a linear programming relaxation of the maximum-likelihood decoding problem. As with many modern decoding algorithms, is possible for the linear programming decoder to output vectors that do not correspond to codewords; such vectors are known as pseudocodewords. In this work, we completely classify the set of linear programming pseudocodewords for the family of cycle codes. For the case of the binary symmetric channel, another approximation of maximum-likelihood decoding was introduced by Omura in 1972. This decoder employs an iterative algorithm whose behavior closely mimics that of the simplex algorithm. We generalize Omura's decoder to operate on any binary-input memoryless channel, thus obtaining a soft-decision decoding algorithm. Further, we prove that the probability of the generalized algorithm returning the maximum-likelihood codeword approaches 1 as the number of iterations goes to infinity.