Stochastic simulation of rare events

Stochastic simulation is an important and practical technique for computing probabilities of rare events, like the payoff probability of a financial option, the probability that a queue exceeds a certain level or the probability of ruin of the insurer's risk process. Rare events occur so infrequently, that they cannot be reasonably recorded during a standard simulation procedure: specifc simulation algorithms which thwart the rarity of the event to simulate are required. An important algorithm in this context is based on changing the sampling distribution and it is called importance sampling. Optimal Monte Carlo algorithms for computing rare event probabilities are either logarithmic eficient or possess bounded relative error.

Monitoring of antiretroviral therapy and mortality in HIV programmes in Malawi, South Africa and Zambia: mathematical modelling study

OBJECTIVES Mortality in patients starting antiretroviral therapy (ART) is higher in Malawi and Zambia than in South Africa. We examined whether different monitoring of ART (viral load [VL] in South Africa and CD4 count in Malawi and Zambia) could explain this mortality difference. DESIGN Mathematical modelling study based on data from ART programmes. METHODS We used a stochastic simulation model to study the effect of VL monitoring on mortality over 5 years. In baseline scenario A all parameters were identical between strategies except for more timely and complete detection of treatment failure with VL monitoring. Additional scenarios introduced delays in switching to second-line ART (scenario B) or higher virologic failure rates (due to worse adherence) when monitoring was based on CD4 counts only (scenario C). Results are presented as relative risks (RR) with 95% prediction intervals and percent of observed mortality difference explained. RESULTS RRs comparing VL with CD4 cell count monitoring were 0.94 (0.74-1.03) in scenario A, 0.94 (0.77-1.02) with delayed switching (scenario B) and 0.80 (0.44-1.07) when assuming a 3-times higher rate of failure (scenario C). The observed mortality at 3 years was 10.9% in Malawi and Zambia and 8.6% in South Africa (absolute difference 2.3%). The percentage of the mortality difference explained by VL monitoring ranged from 4% (scenario A) to 32% (scenarios B and C combined, assuming a 3-times higher failure rate). Eleven percent was explained by non-HIV related mortality. CONCLUSIONS VL monitoring reduces mortality moderately when assuming improved adherence and decreased failure rates.

Economic efficiency analysis of different strategies to control post-weaning multi-systemic wasting syndrome and porcine circovirus type 2 subclinical infection in 3-weekly batch system farms.

The study assessed the economic efficiency of different strategies for the control of post-weaning multi-systemic wasting syndrome (PMWS) and porcine circovirus type 2 subclinical infection (PCV2SI), which have a major economic impact on the pig farming industry worldwide. The control strategies investigated consisted on the combination of up to 5 different control measures. The control measures considered were: (1) PCV2 vaccination of piglets (vac); (2) ensuring age adjusted diet for growers (diets); (3) reduction of stocking density (stock); (4) improvement of biosecurity measures (bios); and (5) total depopulation and repopulation of the farm for the elimination of other major pathogens (DPRP). A model was developed to simulate 5 years production of a pig farm with a 3-weekly batch system and with 100 sows. A PMWS/PCV2SI disease and economic model, based on PMWS severity scores, was linked to the production model in order to assess disease losses. This PMWS severity scores depends on the combination post-weaning mortality, PMWS morbidity in younger pigs and proportion of PCV2 infected pigs observed on farms. The economic analysis investigated eleven different farm scenarios, depending on the number of risk factors present before the intervention. For each strategy, an investment appraisal assessed the extra costs and benefits of reducing a given PMWS severity score to the average score of a slightly affected farm. The net present value obtained for each strategy was then multiplied by the corresponding probability of success to obtain an expected value. A stochastic simulation was performed to account for uncertainty and variability. For moderately affected farms PCV2 vaccination alone was the most cost-efficient strategy, but for highly affected farms it was either PCV2 vaccination alone or in combination with biosecurity measures, with the marginal profitability between 'vac' and 'vac+bios' being small. Other strategies such as 'diets', 'vac+diets' and 'bios+diets' were frequently identified as the second or third best strategy. The mean expected values of the best strategy for a moderately and a highly affected farm were £14,739 and £57,648 after 5 years, respectively. This is the first study to compare economic efficiency of control strategies for PMWS and PCV2SI. The results demonstrate the economic value of PCV2 vaccination, and highlight that on highly affected farms biosecurity measures are required to achieve optimal profitability. The model developed has potential as a farm-level decision support tool for the control of this economically important syndrome.

Reconstruction of a flash flood with large wood transport and its influence on hazard patterns in an ungauged mountain basin

The reconstruction of past flash floods in ungauged basins leads to a high level of uncertainty, which increases if other processes are involved such as the transport of large wood material. An important flash flood occurred in 1997 in Venero Claro (Central Spain), causing significant economic losses. The wood material clogged bridge sections, raising the water level upstream. The aim of this study was to reconstruct this event, analysing the influence of woody debris transport on the flood hazard pattern. Because the reach in question was affected by backwater effects due to bridge clogging, using only high water mark or palaeostage indicators may overestimate discharges, and so other methods are required to estimate peak flows. Therefore, the peak discharge was estimated (123 ± 18 m3 s–1) using indirect methods, but one-dimensional hydraulic simulation was also used to validate these indirect estimates through an iterative process (127 ± 33 m3 s–1) and reconstruct the bridge obstruction to obtain the blockage ratio during the 1997 event (~48%) and the bridge clogging curves. Rainfall–Runoff modelling with stochastic simulation of different rainfall field configurations also helped to confirm that a peak discharge greater than 150 m3 s–1 is very unlikely to occur and that the estimated discharge range is consistent with the estimated rainfall amount (233 ± 27 mm). It was observed that the backwater effect due to the obstruction (water level ~7 m) made the 1997 flood (~35-year return period) equivalent to the 50-year flood. This allowed the equivalent return period to be defined as the recurrence interval of an event of specified magnitude, which, where large woody debris is present, is equivalent in water depth and extent of flooded area to a more extreme event of greater magnitude. These results highlight the need to include obstruction phenomena in flood hazard analysis.

Evidence for Emergency Vaccination Having Played a Crucial Role to Control the 1965/66 Foot-and-Mouth Disease Outbreak in Switzerland.

Foot-and-mouth disease (FMD) is a highly contagious disease that caused several large outbreaks in Europe in the last century. The last important outbreak in Switzerland took place in 1965/66 and affected more than 900 premises and more than 50,000 animals were slaughtered. Large-scale emergency vaccination of the cattle and pig population has been applied to control the epidemic. In recent years, many studies have used infectious disease models to assess the impact of different disease control measures, including models developed for diseases exotic for the specific region of interest. Often, the absence of real outbreak data makes a validation of such models impossible. This study aimed to evaluate whether a spatial, stochastic simulation model (the Davis Animal Disease Simulation model) can predict the course of a Swiss FMD epidemic based on the available historic input data on population structure, contact rates, epidemiology of the virus, and quality of the vaccine. In addition, the potential outcome of the 1965/66 FMD epidemic without application of vaccination was investigated. Comparing the model outcomes to reality, only the largest 10% of the simulated outbreaks approximated the number of animals being culled. However, the simulation model highly overestimated the number of culled premises. While the outbreak duration could not be well reproduced by the model compared to the 1965/66 epidemic, it was able to accurately estimate the size of the area infected. Without application of vaccination, the model predicted a much higher mean number of culled animals than with vaccination, demonstrating that vaccination was likely crucial in disease control for the Swiss FMD outbreak in 1965/66. The study demonstrated the feasibility to analyze historical outbreak data with modern analytical tools. However, it also confirmed that predicted epidemics from a most carefully parameterized model cannot integrate all eventualities of a real epidemic. Therefore, decision makers need to be aware that infectious disease models are useful tools to support the decision-making process but their results are not equal valuable as real observations and should always be interpreted with caution.

Evaluation of control and surveillance strategies for classical swine fever using a simulation model

Classical swine fever (CSF) outbreaks can cause enormous losses in naïve pig populations. How to best minimize the economic damage and number of culled animals caused by CSF is therefore an important research area. The baseline CSF control strategy in the European Union and Switzerland consists of culling all animals in infected herds, movement restrictions for animals, material and people within a given distance to the infected herd and epidemiological tracing of transmission contacts. Additional disease control measures such as pre-emptive culling or vaccination have been recommended based on the results from several simulation models; however, these models were parameterized for areas with high animal densities. The objective of this study was to explore whether pre-emptive culling and emergency vaccination should also be recommended in low- to moderate-density areas such as Switzerland. Additionally, we studied the influence of initial outbreak conditions on outbreak severity to improve the efficiency of disease prevention and surveillance. A spatial, stochastic, individual-animal-based simulation model using all registered Swiss pig premises in 2009 (n=9770) was implemented to quantify these relationships. The model simulates within-herd and between-herd transmission (direct and indirect contacts and local area spread). By varying the four parameters (a) control measures, (b) index herd type (breeding, fattening, weaning or mixed herd), (c) detection delay for secondary cases during an outbreak and (d) contact tracing probability, 112 distinct scenarios were simulated. To assess the impact of scenarios on outbreak severity, daily transmission rates were compared between scenarios. Compared with the baseline strategy (stamping out and movement restrictions) vaccination and pre-emptive culling neither reduced outbreak size nor duration. Outbreaks starting in a herd with weaning piglets or fattening pigs caused higher losses regarding to the number of culled premises and were longer lasting than those starting in the two other index herd types. Similarly, larger transmission rates were estimated for these index herd type outbreaks. A longer detection delay resulted in more culled premises and longer duration and better transmission tracing increased the number of short outbreaks. Based on the simulation results, baseline control strategies seem sufficient to control CSF in low-medium animal-dense areas. Early detection of outbreaks is crucial and risk-based surveillance should be focused on weaning piglet and fattening pig premises.

Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment.

Domestic dog rabies is an endemic disease in large parts of the developing world and also epidemic in previously free regions. For example, it continues to spread in eastern Indonesia and currently threatens adjacent rabies-free regions with high densities of free-roaming dogs, including remote northern Australia. Mathematical and simulation disease models are useful tools to provide insights on the most effective control strategies and to inform policy decisions. Existing rabies models typically focus on long-term control programs in endemic countries. However, simulation models describing the dog rabies incursion scenario in regions where rabies is still exotic are lacking. We here describe such a stochastic, spatially explicit rabies simulation model that is based on individual dog information collected in two remote regions in northern Australia. Illustrative simulations produced plausible results with epidemic characteristics expected for rabies outbreaks in disease free regions (mean R0 1.7, epidemic peak 97 days post-incursion, vaccination as the most effective response strategy). Systematic sensitivity analysis identified that model outcomes were most sensitive to seven of the 30 model parameters tested. This model is suitable for exploring rabies spread and control before an incursion in populations of largely free-roaming dogs that live close together with their owners. It can be used for ad-hoc contingency or response planning prior to and shortly after incursion of dog rabies in previously free regions. One challenge that remains is model parameterisation, particularly how dogs' roaming and contacts and biting behaviours change following a rabies incursion in a previously rabies free population.