Capturing the time-varying drivers of an epidemic using stochastic dynamical systems

Epidemics are often modelled using non-linear dynamical systems observed through partial and noisy data. In this paper, we consider stochastic extensions in order to capture unknown influences (changing behaviors, public interventions, seasonal effects etc). These models assign diffusion processes to the time-varying parameters, and our inferential procedure is based on a suitably adjusted adaptive particle MCMC algorithm. The performance of the proposed computational methods is validated on simulated data and the adopted model is applied to the 2009 H1N1 pandemic in England. In addition to estimating the effective contact rate trajectories, the methodology is applied in real time to provide evidence in related public health decisions. Diffusion driven SEIR-type models with age structure are also introduced.Comment: 21 pages, 5 figure

Complex temporal climate signals drive the emergence of human water-borne disease

Predominantly occurring in developing parts of the world, Buruli ulcer is a severely disabling mycobacterium infection which often leads to extensive necrosis of the skin. While the exact route of transmission remains uncertain, like many tropical diseases, associations with climate have been previously observed and could help identify the causative agent's ecological niche. In this paper, links between changes in rainfall and outbreaks of Buruli ulcer in French Guiana, an ultraperipheral European territory in the northeast of South America, were identified using a combination of statistical tests based on singular spectrum analysis, empirical mode decomposition and cross-wavelet coherence analysis. From this, it was possible to postulate for the first time that outbreaks of Buruli ulcer can be triggered by combinations of rainfall patterns occurring on a long (i.e., several years) and short (i.e., seasonal) temporal scale, in addition to stochastic events driven by the El Nino-Southern Oscillation that may disrupt or interact with these patterns. Long-term forecasting of rainfall trends further suggests the possibility of an upcoming outbreak of Buruli ulcer in French Guiana

Rhythmic dynamics and synchronization via dimensionality reduction : application to human gait

Reliable characterization of locomotor dynamics of human walking is vital to understanding the neuromuscular control of human locomotion and disease diagnosis. However, the inherent oscillation and ubiquity of noise in such non-strictly periodic signals pose great challenges to current methodologies. To this end, we exploit the state-of-the-art technology in pattern recognition and, specifically, dimensionality reduction techniques, and propose to reconstruct and characterize the dynamics accurately on the cycle scale of the signal. This is achieved by deriving a low-dimensional representation of the cycles through global optimization, which effectively preserves the topology of the cycles that are embedded in a high-dimensional Euclidian space. Our approach demonstrates a clear advantage in capturing the intrinsic dynamics and probing the subtle synchronization patterns from uni/bivariate oscillatory signals over traditional methods. Application to human gait data for healthy subjects and diabetics reveals a significant difference in the dynamics of ankle movements and ankle-knee coordination, but not in knee movements. These results indicate that the impaired sensory feedback from the feet due to diabetes does not influence the knee movement in general, and that normal human walking is not critically dependent on the feedback from the peripheral nervous system

Regional-scale climate-variability synchrony of cholera epidemics in West Africa

BACKGROUND: The relationship between cholera and climate was explored in Africa, the continent with the most reported cases, by analyzing monthly 20-year cholera time series for five coastal adjoining West African countries: Côte d'Ivoire, Ghana, Togo, Benin and Nigeria. METHODS: We used wavelet analyses and derived methods because these are useful mathematical tools to provide information on the evolution of the periodic component over time and allow quantification of non-stationary associations between time series. RESULTS: The temporal variability of cholera incidence exhibits an interannual component, and a significant synchrony in cholera epidemics is highlighted at the end of the 1980's. This observed synchrony across countries, even if transient through time, is also coherent with both the local variability of rainfall and the global climate variability quantified by the Indian Oscillation Index. CONCLUSION: Results of this study suggest that large and regional scale climate variability influence both the temporal dynamics and the spatial synchrony of cholera epidemics in human populations in the Gulf of Guinea, as has been described for two other tropical regions of the world, western South America and Bangladesh

Long-term species, sexual and individual variations in foraging strategies of fur seals revealed by stable isotopes in whiskers

Background: Individual variations in the use of the species niche are an important component of diversity in trophic interactions. A challenge in testing consistency of individual foraging strategy is the repeated collection of information on the same individuals. Methodology/Principal Findings: The foraging strategies of sympatric fur seals (Arctocephalus gazella and A. tropicalis) were examined using the stable isotope signature of serially sampled whiskers. Most whiskers exhibited synchronous delta C-13 and delta N-15 oscillations that correspond to the seal annual movements over the long term (up to 8 years). delta C-13 and delta N-15 values were spread over large ranges, with differences between species, sexes and individuals. The main segregating mechanism operates at the spatial scale. Most seals favored foraging in subantarctic waters (where the Crozet Islands are located) where they fed on myctophids. However, A. gazella dispersed in the Antarctic Zone and A. tropicalis more in the subtropics. Gender differences in annual time budget shape the seal movements. Males that do not perform any parental care exhibited large isotopic oscillations reflecting broad annual migrations, while isotopic values of females confined to a limited foraging range during lactation exhibited smaller changes. Limited inter-individual isotopic variations occurred in female seals and in male A. tropicalis. In contrast, male A. gazella showed large inter-individual variations, with some males migrating repeatedly to high-Antarctic waters where they fed on krill, thus meaning that individual specialization occurred over years. Conclusions/Significance: Whisker isotopic signature yields unique long-term information on individual behaviour that integrates the spatial, trophic and temporal dimensions of the ecological niche. The method allows depicting the entire realized niche of the species, including some of its less well-known components such as age-, sex-, individual- and migration-related changes. It highlights intrapopulation heterogeneity in foraging strategies that could have important implications for likely demographic responses to environmental variability

WAVOS: a MATLAB toolkit for wavelet analysis and visualization of oscillatory systems

<p>Abstract</p> <p>Background</p> <p>Wavelets have proven to be a powerful technique for the analysis of periodic data, such as those that arise in the analysis of circadian oscillators. While many implementations of both continuous and discrete wavelet transforms are available, we are aware of no software that has been designed with the nontechnical end-user in mind. By developing a toolkit that makes these analyses accessible to end users without significant programming experience, we hope to promote the more widespread use of wavelet analysis.</p> <p>Findings</p> <p>We have developed the WAVOS toolkit for wavelet analysis and visualization of oscillatory systems. WAVOS features both the continuous (Morlet) and discrete (Daubechies) wavelet transforms, with a simple, user-friendly graphical user interface within MATLAB. The interface allows for data to be imported from a number of standard file formats, visualized, processed and analyzed, and exported without use of the command line. Our work has been motivated by the challenges of circadian data, thus default settings appropriate to the analysis of such data have been pre-selected in order to minimize the need for fine-tuning. The toolkit is flexible enough to deal with a wide range of oscillatory signals, however, and may be used in more general contexts.</p> <p>Conclusions</p> <p>We have presented WAVOS: a comprehensive wavelet-based MATLAB toolkit that allows for easy visualization, exploration, and analysis of oscillatory data. WAVOS includes both the Morlet continuous wavelet transform and the Daubechies discrete wavelet transform. We have illustrated the use of WAVOS, and demonstrated its utility for the analysis of circadian data on both bioluminesence and wheel-running data. WAVOS is freely available at <url>http://sourceforge.net/projects/wavos/files/</url></p

Impacts of El Niño Southern Oscillation and Indian Ocean Dipole on dengue incidence in Bangladesh

Dengue dynamics are driven by complex interactions between hosts, vectors and viruses that are influenced by environmental and climatic factors. Several studies examined the role of El Niño Southern Oscillation (ENSO) in dengue incidence. However, the role of Indian Ocean Dipole (IOD), a coupled ocean atmosphere phenomenon in the Indian Ocean, which controls the summer monsoon rainfall in the Indian region, remains unexplored. Here, we examined the effects of ENSO and IOD on dengue incidence in Bangladesh. According to the wavelet coherence analysis, there was a very weak association between ENSO, IOD and dengue incidence, but a highly significant coherence between dengue incidence and local climate variables (temperature and rainfall). However, a distributed lag nonlinear model (DLNM) revealed that the association between dengue incidence and ENSO or IOD were comparatively stronger after adjustment for local climate variables, seasonality and trend. The estimated effects were nonlinear for both ENSO and IOD with higher relative risks at higher ENSO and IOD. The weak association between ENSO, IOD and dengue incidence might be driven by the stronger effects of local climate variables such as temperature and rainfall. Further research is required to disentangle these effects

Forcing Versus Feedback: Epidemic Malaria and Monsoon Rains in Northwest India

Malaria epidemics in regions with seasonal windows of transmission can vary greatly in size from year to year. A central question has been whether these interannual cycles are driven by climate, are instead generated by the intrinsic dynamics of the disease, or result from the resonance of these two mechanisms. This corresponds to the more general inverse problem of identifying the respective roles of external forcings vs. internal feedbacks from time series for nonlinear and noisy systems. We propose here a quantitative approach to formally compare rival hypotheses on climate vs. disease dynamics, or external forcings vs. internal feedbacks, that combines dynamical models with recently developed, computational inference methods. The interannual patterns of epidemic malaria are investigated here for desert regions of northwest India, with extensive epidemiological records for Plasmodium falciparum malaria for the past two decades. We formulate a dynamical model of malaria transmission that explicitly incorporates rainfall, and we rely on recent advances on parameter estimation for nonlinear and stochastic dynamical systems based on sequential Monte Carlo methods. Results show a significant effect of rainfall in the inter-annual variability of epidemic malaria that involves a threshold in the disease response. The model exhibits high prediction skill for yearly cases in the malaria transmission season following the monsoonal rains. Consideration of a more complex model with clinical immunity demonstrates the robustness of the findings and suggests a role of infected individuals that lack clinical symptoms as a reservoir for transmission. Our results indicate that the nonlinear dynamics of the disease itself play a role at the seasonal, but not the interannual, time scales. They illustrate the feasibility of forecasting malaria epidemics in desert and semi-arid regions of India based on climate variability. This approach should be applicable to malaria in other locations, to other infectious diseases, and to other nonlinear systems under forcing

Local and Global Effects of Climate on Dengue Transmission in Puerto Rico

The four dengue viruses, the agents of dengue fever and dengue hemorrhagic fever in humans, are transmitted predominantly by the mosquito Aedes aegypti. The abundance and the transmission potential of Ae. aegypti are influenced by temperature and precipitation. While there is strong biological evidence for these effects, empirical studies of the relationship between climate and dengue incidence in human populations are potentially confounded by seasonal covariation and spatial heterogeneity. Using 20 years of data and a statistical approach to control for seasonality, we show a positive and statistically significant association between monthly changes in temperature and precipitation and monthly changes in dengue transmission in Puerto Rico. We also found that the strength of this association varies spatially, that this variation is associated with differences in local climate, and that this relationship is consistent with laboratory studies of the impacts of these factors on vector survival and viral replication. These results suggest the importance of temperature and precipitation in the transmission of dengue viruses and suggest a reason for their spatial heterogeneity. Thus, while dengue transmission may have a general system, its manifestation on a local scale may differ from global expectations

Probabilistic Daily ILI Syndromic Surveillance with a Spatio-Temporal Bayesian Hierarchical Model

BACKGROUND: For daily syndromic surveillance to be effective, an efficient and sensible algorithm would be expected to detect aberrations in influenza illness, and alert public health workers prior to any impending epidemic. This detection or alert surely contains uncertainty, and thus should be evaluated with a proper probabilistic measure. However, traditional monitoring mechanisms simply provide a binary alert, failing to adequately address this uncertainty. METHODS AND FINDINGS: Based on the Bayesian posterior probability of influenza-like illness (ILI) visits, the intensity of outbreak can be directly assessed. The numbers of daily emergency room ILI visits at five community hospitals in Taipei City during 2006-2007 were collected and fitted with a Bayesian hierarchical model containing meteorological factors such as temperature and vapor pressure, spatial interaction with conditional autoregressive structure, weekend and holiday effects, seasonality factors, and previous ILI visits. The proposed algorithm recommends an alert for action if the posterior probability is larger than 70%. External data from January to February of 2008 were retained for validation. The decision rule detects successfully the peak in the validation period. When comparing the posterior probability evaluation with the modified Cusum method, results show that the proposed method is able to detect the signals 1-2 days prior to the rise of ILI visits. CONCLUSIONS: This Bayesian hierarchical model not only constitutes a dynamic surveillance system but also constructs a stochastic evaluation of the need to call for alert. The monitoring mechanism provides earlier detection as well as a complementary tool for current surveillance programs