Rapid simulation of spatial epidemics : a spectral method

Spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In the majority of situations, it is only possible to predict the spatial spread of infection using simulation models, which can be computationally demanding especially for large population sizes. Here we develop an approximation method that vastly reduces this computational burden. We assume that the transmission rates between individuals or sub-populations are determined by a spatial transmission kernel. This kernel is assumed to be isotropic, such that the transmission rate is simply a function of the distance between susceptible and infectious individuals; as such this provides the ideal mechanism for modelling localised transmission in a spatial environment. We show that the spatial force of infection acting on all susceptibles can be represented as a spatial convolution between the transmission kernel and a spatially extended ‘image’ of the infection state. This representation allows the rapid calculation of stochastic rates of infection using fast-Fourier transform (FFT) routines, which greatly improves the computational efficiency of spatial simulations. We demonstrate the efficiency and accuracy of this fast spectral rate recalculation (FSR) method with two examples: an idealised scenario simulating an SIR-type epidemic outbreak amongst N habitats distributed across a two-dimensional plane; the spread of infection between US cattle farms, illustrating that the FSR method makes continental-scale outbreak forecasting feasible with desktop processing power. The latter model demonstrates which areas of the US are at consistently high risk for cattle-infections, although predictions of epidemic size are highly dependent on assumptions about the tail of the transmission kernel

Aggregation dynamics explain vegetation patch-size distributions

Vegetation patch-size distributions have been an intense area of study for theoreticians and applied ecologists alike in recent years. Of particular interest is the seemingly ubiquitous nature of power-law patch-size distributions emerging in a number of diverse ecosystems. The leading explanation of the emergence of these power-laws is due to local facilitative mechanisms. There is also a common transition from power law to exponential distribution when a system is under global pressure, such as grazing or lack of rainfall. These phenomena require a simple mechanistic explanation. Here, we study vegetation patches from a spatially implicit, patch dynamic viewpoint. We show that under minimal assumptions a power-law patch-size distribution appears as a natural consequence of aggregation. A linear death term also leads to an exponential term in the distribution for any non-zero death rate. This work shows the origin of the breakdown of the power-law under increasing pressure and shows that in general, we expect to observe a power law with an exponential cutoff (rather than pure power laws). The estimated parameters of this distribution also provide insight into the underlying ecological mechanisms of aggregation and death

Disentangling the influence of livestock vs. farm density on livestock disease epidemics

Susceptible host density is a key factor that influences the success of invading pathogens. However, for diseases affecting livestock, there are two aspects of host density: livestock and farm density, which are seldom considered independently. Traditional approaches of simulating disease outbreaks on real‐world farm data make dissecting the relative importance of farm and livestock density difficult owing to their inherent correlation in many farming regions. We took steps to disentangle these densities and study their relative influences on epidemic size by simulating foot‐and‐mouth disease outbreaks on factorial combinations of cattle and farm populations in artificial county areas, resulting in 50 unique cattle/farm density combinations. In these simulations, increasing cattle density always resulted in larger epidemics, regardless of farm density. Alternatively, increasing farm density only led to larger epidemics in scenarios of high cattle density. We compared these results with simulations performed on real‐world farm data from the United States, where we initiated outbreaks in U.S. counties that varied in county‐level cattle density and farm density. We found a similar, but weaker relationship between cattle density and epidemic size in the U.S. simulations. We tested the sensitivity of these outcomes to variation in pathogen dispersal and farm‐level susceptibility model parameters and found that although variation in these parameters quantitatively influenced the size of the epidemic, they did not qualitatively change the relative influence of cattle vs. farm density in factorial simulations. By reducing the correlation between farm and livestock density in factorial simulations, we were able to clearly demonstrate the increase in epidemic size that occurred as farm sizes grew larger (i.e., through increasing county‐level cattle populations), across levels of farm density. These results suggest livestock production trends in many industrialized countries that concentrate livestock on fewer, but larger farms have the potential to facilitate larger livestock epidemics

Topographic determinants of foot and mouth disease transmission in the UK 2001 epidemic

Background A key challenge for modelling infectious disease dynamics is to understand the spatial spread of infection in real landscapes. This ideally requires a parallel record of spatial epidemic spread and a detailed map of susceptible host density along with relevant transport links and geographical features. Results Here we analyse the most detailed such data to date arising from the UK 2001 foot and mouth epidemic. We show that Euclidean distance between infectious and susceptible premises is a better predictor of transmission risk than shortest and quickest routes via road, except where major geographical features intervene. Conclusion Thus, a simple spatial transmission kernel based on Euclidean distance suffices in most regions, probably reflecting the multiplicity of transmission routes during the epidemic

Predicting the impact of intervention strategies for sleeping sickness in two high-endemicity health zones of the Democratic Republic of Congo

Two goals have been set for Gambian human African trypanosomiasis (HAT), the first is to achieve elimination as a public health problem in 90% of foci by 2020, and the second is to achieve zero transmission globally by 2030. It remains unclear if certain HAT hotspots could achieve elimination as a public health problem by 2020 and, of greater concern, it appears that current interventions to control HAT in these areas may not be sufficient to achieve zero transmission by 2030. A mathematical model of disease dynamics was used to assess the potential impact of changing the intervention strategy in two high-endemicity health zones of Kwilu province, Democratic Republic of Congo. Six key strategies and twelve variations were considered which covered a range of recruitment strategies for screening and vector control. It was found that effectiveness of HAT screening could be improved by increasing effort to recruit high-risk groups for screening. Furthermore, seven proposed strategies which included vector control were predicted to be sufficient to achieve an incidence of less than 1 reported case per 10,000 people by 2020 in the study region. All vector control strategies simulated reduced transmission enough to meet the 2030 goal, even if vector control was only moderately effective (60% tsetse population reduction). At this level of control the full elimination threshold was expected to be met within six years following the start of the change in strategy and over 6000 additional cases would be averted between 2017 and 2030 compared to current screening alone. It is recommended that a two-pronged strategy including both enhanced active screening and tsetse control is implemented in this region and in other persistent HAT foci to ensure the success of the control programme and meet the 2030 elimination goal for HAT

Climate drivers of plague epidemiology in British India, 1898–1949

Plague, caused by Yersinia pestis infection, continues to threaten low- and middle-income countries throughout the world. The complex interactions between rodents and fleas with their respective environments challenge our understanding of human plague epidemiology. Historical long-term datasets of reported plague cases offer a unique opportunity to elucidate the effects of climate on plague outbreaks in detail. Here, we analyse monthly plague deaths and climate data from 25 provinces in British India from 1898 to 1949 to generate insights into the influence of temperature, rainfall and humidity on the occurrence, severity and timing of plague outbreaks. We find that moderate relative humidity levels of between 60% and 80% were strongly associated with outbreaks. Using wavelet analysis, we determine that the nationwide spread of plague was driven by changes in humidity, where, on average, a one-month delay in the onset of rising humidity translated into a one-month delay in the timing of plague outbreaks. This work can inform modern spatio-temporal predictive models for the disease and aid in the development of early-warning strategies for the deployment of prophylactic treatments and other control measures

Performance of an environmental test to detect Mycobacterium bovis infection in badger social groups

A study by Courtenay and others (2006) demonstrated that the probability of detecting Mycobacterium bovis by PCR in soil samples from the spoil heaps of main badger setts correlated with the prevalence of excretion (infectiousness) of captured badgers belonging to the social group. It has been proposed that such a test could be used to target badger culling to setts containing infectious animals (Anon 2007). This short communication discusses the issues surrounding this concept, with the intention of dispelling any misconceptions among relevant stakeholders (farmers, policy makers and conservationists)

Disease transmission promotes evolution of host spatial patterns

Ecological dynamics can produce a variety of striking patterns. On ecological time scales, pattern formation has been hypothesized to be due to the interaction between a species and its local environment. On longer time scales, evolutionary factors must be taken into account. To examine the evolutionary robustness of spatial pattern formation, we construct a spatially explicit model of vegetation in the presence of a pathogen. Initially, we compare the dynamics for vegetation parameters that lead to competition induced spatial patterns and those that do not. Over ecological time scales, banded spatial patterns dramatically reduced the ability of the pathogen to spread, lowered its endemic density and hence increased the persistence of the vegetation. To gain an evolutionary understanding, each plant was given a heritable trait defining its resilience to competition; greater competition leads to lower vegetation density but stronger spatial patterns. When a disease is introduced, the selective pressure on the plant's resilience to the competition parameter is determined by the transmission of the disease. For high transmission, vegetation that has low resilience to competition and hence strong spatial patterning is an evolutionarily stable strategy. This demonstrates a novel mechanism by which striking spatial patterns can be maintained by disease-driven selection

Modelling the impact of local reactive school closures on critical care provision during an influenza pandemic

Despite the fact that the 2009 H1N1 pandemic influenza strain was less severe than had been feared, both seasonal epidemics of influenza-like-illness and future influenza pandemics have the potential to place a serious burden on health services. The closure of schools has been postulated as a means of reducing transmission between children and hence reducing the number of cases at the peak of an epidemic; this is supported by the marked reduction in cases during school holidays observed across the world during the 2009 pandemic. However, a national policy of long-duration school closures could have severe economic costs. Reactive short-duration closure of schools in regions where health services are close to capacity offers a potential compromise, but it is unclear over what spatial scale and time frame closures would need to be made to be effective. Here, using detailed geographical information for England, we assess how localized school closures could alleviate the burden on hospital intensive care units (ICUs) that are reaching capacity. We show that, for a range of epidemiologically plausible assumptions, considerable local coordination of school closures is needed to achieve a substantial reduction in the number of hospitals where capacity is exceeded at the peak of the epidemic. The heterogeneity in demand per hospital ICU bed means that even widespread school closures are unlikely to have an impact on whether demand will exceed capacity for many hospitals. These results support the UK decision not to use localized school closures as a control mechanism, but have far wider international public-health implications. The spatial heterogeneities in both population density and hospital capacity that give rise to our results exist in many developed countries, while our model assumptions are sufficiently general to cover a wide range of pathogens. This leads us to believe that when a pandemic has severe implications for ICU capacity, only widespread school closures (with their associated costs and organizational challenges) are sufficient to mitigate the burden on the worst-affected hospitals

Cattle farmer psychosocial profiles and their association with control strategies for bovine viral diarrhea

Bovine viral diarrhea (BVD) is endemic in the United Kingdom and causes major economic losses. Control is largely voluntary for individual farmers and is likely to be influenced by psychosocial factors, such as altruism, trust, and psychological proximity (feeling close) to relevant “others,” such as farmers, veterinarians, the government, and their cows. These psychosocial factors (factors with both psychological and social aspects) are important determinants of how people make decisions related to their own health, many of which have not been studied in the context of infectious disease control by farmers. Farmer psychosocial profiles were investigated using multiple validated measures in an observational survey of 475 UK cattle farmers using the capability, opportunity, motivation-behavior (COM-B) framework. Farmers were clustered by their BVD control practices using latent class analysis. Farmers were split into 5 BVD control behavior classes, which were tested for associations with the psychosocial and COM-B factors using multinomial logistic regression, with doing nothing as the baseline class. Farmers who were controlling disease both for themselves and others were more likely to do something to control BVD (e.g., test, vaccinate). Farmers who did not trust other farmers, had high psychological capability (knowledge and understanding of how to control disease), and had high physical opportunity (time and money to control disease) were more likely to have a closed, separate herd and test. Farmers who did not trust other farmers were also more likely to undertake many prevention strategies with an open herd. Farmers with high automatic motivation (habits and emotions) and reflective motivation (decisions and goals) were more likely to vaccinate and test, alone or in combination with other controls. Farmers with high psychological proximity (feeling of closeness) to their veterinarian were more likely to undertake many prevention strategies in an open herd. Farmers with high psychological proximity to dairy farmers and low psychological proximity to beef farmers were more likely to keep their herd closed and separate and test or vaccinate and test. Farmers who had a lot of trust in other farmers and invested in them, rather than keeping everything for themselves, were more likely to be careful introducing new stock and test. In conclusion, farmer psychosocial factors were associated with strategies for BVD control in UK cattle farmers. Psychological proximity to veterinarians was a novel factor associated with proactive BVD control and was more important than the more extensively investigated trust. These findings highlight the importance of a close veterinarian-farmer relationship and are important for promoting effective BVD control by farmers, which has implications for successful nationwide BVD control and eradication schemes