Mathematical Models for Estimating the Risks of Bovine Spongiform Encephalopathy (BSE).

When the bovine spongiform encephalopathy (BSE) epidemic first emerged in the United Kingdom in the mid 1980s, the etiology of animal prion diseases was largely unknown. Risk management efforts to control the disease were also subject to uncertainties regarding the extent of BSE infections and future course of the epidemic. As understanding of BSE increased, mathematical models were developed to estimate risk of BSE infection and to predict reductions in risk in response to BSE control measures. Risk models of BSE-transmission dynamics determined disease persistence in cattle herds and relative infectivity of cattle prior to onset of clinical disease. These BSE models helped in understanding key epidemiological features of BSE transmission and dynamics, such as incubation period distribution and age-dependent infection susceptibility to infection with the BSE agent. This review summarizes different mathematical models and methods that have been used to estimate risk of BSE, and discusses how such risk projection models have informed risk assessment and management of BSE. This review also provides some general insights on how mathematical models of the type discussed here may be used to estimate risks of emerging zoonotic diseases when biological data on transmission of the etiological agent are limited.

Hysteresis in a quantized superfluid 'atomtronic' circuit.

Atomtronics is an emerging interdisciplinary field that seeks to develop new functional methods by creating devices and circuits where ultracold atoms, often superfluids, have a role analogous to that of electrons in electronics. Hysteresis is widely used in electronic circuits-it is routinely observed in superconducting circuits and is essential in radio-frequency superconducting quantum interference devices. Furthermore, it is as fundamental to superfluidity (and superconductivity) as quantized persistent currents, critical velocity and Josephson effects. Nevertheless, despite multiple theoretical predictions, hysteresis has not been previously observed in any superfluid, atomic-gas Bose-Einstein condensate. Here we directly detect hysteresis between quantized circulation states in an atomtronic circuit formed from a ring of superfluid Bose-Einstein condensate obstructed by a rotating weak link (a region of low atomic density). This contrasts with previous experiments on superfluid liquid helium where hysteresis was observed directly in systems in which the quantization of flow could not be observed, and indirectly in systems that showed quantized flow. Our techniques allow us to tune the size of the hysteresis loop and to consider the fundamental excitations that accompany hysteresis. The results suggest that the relevant excitations involved in hysteresis are vortices, and indicate that dissipation has an important role in the dynamics. Controlled hysteresis in atomtronic circuits may prove to be a crucial feature for the development of practical devices, just as it has in electronic circuits such as memories, digital noise filters (for example Schmitt triggers) and magnetometers (for example superconducting quantum interference devices).

Impact of potential changes to the current bovine spongiform encephalopathy surveillance programs for slaughter cattle and fallen stock in Japan.

Cattle slaughtered in Japan for human consumption, regardless of their age, have been tested for bovine spongiform encephalopathy (BSE) since October 2001. Beginning in April 2004, all fallen stock from 24 months of age also have been tested. We evaluated the impact of potential changes to the current BSE surveillance programs for both slaughter cattle and fallen stock using a simple stochastic model. We calculated the probability that a BSE-infected dairy cow, Wagyu beef animal, Wagyu-Holstein cross steer or heifer, or Holstein steer slaughtered for human consumption or arising as fallen stock would be tested and detected. Four surveillance strategies were explored for cattle slaughtered for human consumption, with the minimum age at testing set at 0, 21, 31, or 41 months. Three surveillance strategies were explored for fallen stock, with the minimum age at testing set at 24, 31, or 41 months. Increasing the minimum age of testing from 0 to 21 months for both dairy cattle and Wagyu beef cattle had very little impact on the probability that a BSE-infected animal slaughtered for human consumption would be detected. Although increasing the minimum age at testing from 21 to 31 or 41 months would lead to fewer slaughtered animals being tested, the impact on the probability of detecting infected animals would be insignificant. The probability of infected Wagyu-Holstein crosses and Holstein steers being detected at slaughter or as fallen stock would be very low under all surveillance strategies.

Simulating the BSE epidemic and multiplication factor in dairy herds in Japan.

With the objective of evaluating the effectiveness of an administrative guidance on the use of ruminant meat-and-bone meal in ruminant feed, effective from April 1996 to September 2001, we developed a model to simulate the evolution of the BSE epidemic and to estimate the BSE multiplication factor (K) in the Japanese dairy population. The output that provided the best fit to the number of BSE cases both observed and predicted to date suggest that the probability that bovine MBM was fed back to cattle was 14.2-75.2% and 0.129-0.570% during the periods from 1992 to April 1996 and from April 1996 to October 2001, respectively. Given these estimates, the value of K would have peaked in 1995 at 40-48 and then declined to 0.32-0.67 between 1997 and 2001. These results suggest that the administrative guidance was effective in reducing the amount of MBM fed to cattle by a factor of 104-141 and was perhaps enough to drive the epidemic towards extinction.

Estimating the prevalence of BSE in dairy birth cohorts and predicting the incidence of BSE cases in Japan.

Following the detection of the first case of BSE in Japan in September 2001, four million cattle were subjected to a rapid test for BSE up to the end of 2004. A further 10 cases were detected in the dairy cattle population and two cases in Holstein steers. We focused on the dairy population and estimated the prevalence of BSE infected animals within each birth cohort for the years 1992-2001 using Bayesian inference. From this we were able to predict historic and future trends in the number of infected animals culled from each cohort and whether or not they could be detected using a rapid test. Assuming that BSE infectivity entered Japan in 1995, 225 (95%CI: 111-418) infected animals were predicted to have been culled from 1995 to 2001, of which 116 (56-219) would have been slaughtered for human consumption, and 33 (12-65) cases would have been detected during this period if a BSE surveillance program as comprehensive as the one in place as of April 2004 was applied. Assuming that BSE infectivity entered Japan in 1992, 905 (366-4633) infected animals were predicted to have been culled from 1992 to 2001, of which 694 (190-2473) would have been slaughtered for human consumption, and 201 (53-693) cases would have been detected during this period. Assuming the April 2004 level of surveillance continues and that the feed ban introduced in 2001 is completely effective, 18 (3-111) BSE cases are likely to be detected in the future. The BSE epidemic in Japan most likely reached a peak between 1998 and 2001 and should be eradicated around 2012.