The transmission of many infectious diseases is affected by climate variations, particularly for diseases spread by arthropod vectors such as malaria and dengue. Previous epidemiological studies have demonstrated statistically significant associations between infectious disease incidence and climate variations. Such research has highlighted the potential for developing climate-based epidemic early warning systems. To establish how much variation in disease risk can be attributed to climatic conditions, non-climatic confounding factors should also be considered in the model parameterisation to avoid reporting misleading climate-disease associations. This issue is sometimes overlooked in climate related disease studies. Due to the lack of spatial resolution and/or the capability to predict future disease risk (e.g. several months ahead), some previous models are of limited value for public health decision making. This thesis proposes a framework to model spatio-temporal variation in disease risk using both climate and non-climate information. The framework is developed in the context of dengue fever in Brazil. Dengue is currently one of the most important emerging tropical diseases and dengue epidemics impact heavily on Brazilian public health services. A negative binomial generalised linear mixed model (GLMM) is adopted which makes allowances for unobserved confounding factors by including spatially structured and unstructured random effects. The model successfully accounts for the large amount of overdispersion found in disease counts. The parameters in this spatio-temporal Bayesian hierarchical model are estimated using Markov Chain Monte Carlo (MCMC). This allows posterior predictive distributions for disease risk to be derived for each spatial location and time period (month/season). Given decision and epidemic thresholds, probabilistic forecasts can be issued, which are useful for developing epidemic early warning systems. The potential to provide useful early warnings of future increased and geographically specific dengue risk is investigated. The predictive validity of the model is evaluated by fitting the GLMM to data from 2001-2007 and comparing probabilistic predictions to the most recent out-of-sample data in 2008-2009. For a probability decision threshold of 30% and the pre-defined epidemic threshold of 300 cases per 100,000 inhabitants, successful epidemic alerts would have been issued for 94% of the 54 microregions that experienced high dengue incidence rates in South East Brazil, during February - April 2008.

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The environmental risk of growing genetically modified (GM) crops and particularly the spreading of GM genes to related non-GM crops is currently a concern in European agriculture. Because the risks of contamination are linked to the spatial and temporal arrangements of crops within the landscape, scenarios of crop arrangement are required to investigate the risks and potential coexistence measures. However, until recently, only manual methods were available to create scenarios. This thesis aims to provide a flexible referenced tool to create such scenarios. The model, called LandSFACTS, is a scientific research tool which allocates crops into fields, to meet user-defined crop spatio-temporal arrangements, using an empirical and statistical approach. The control of the crop arrangements is divided into two main sections: (i) the temporal arrangement of crops: encompassing crop rotations as transition matrices (specifically-developed methodology), temporal constraints (return period of crops, forbidden crop sequences), initial crops in fields regulated by temporal patterns (specifically-developed statistical analyses) and yearly crop proportions; and (ii) the spatial arrangements of crops: encompassing possible crops in fields, crop rotation in fields regulated by spatial patterns (specifically-developed statistical analyses), and spatial constraints (separation distances between crops). The limitations imposed by the model include the size of the smallest spatial and temporal unit: only one crop is allocated per field and per year. The model has been designed to be used by researchers with agronomic knowledge of the landscape. An assessment of the model did not lead to the detection of any significant flaws and therefore the model is considered valid for the stated specifications. Following this evaluation, the model is being used to fill incomplete datasets, build up and compare scenarios of crop allocations. Within the GM coexistence context, the model could provide useful support to investigate the impact of crop arrangement and potential coexistence measures on the risk of GM contamination of crops. More informed advice could therefore be provided to decision makers on the feasibility and efficiency of coexistence measures for GM cultivation.

Stroke is a major cause of disability and death worldwide. Although different clinical studies and trials used Magnetic Resonance Imaging (MRI) to examine patterns of change in different imaging modalities (eg: perfusion and diffusion), we still lack a clear and definite answer to the question: “How does an acute ischemic stroke lesion grow?” The inability to distinguish viable and dead tissue in abnormal MR regions in stroke patients weakens the evidence accumulated to answer this question, and relying on static snapshots of patient scans to fill in the spatio-temporal gaps by “thinking/guessing” make it even harder to tackle. Different opposing observations undermine our understanding of ischemic stroke evolution, especially at the acute stage: viable tissue transiting into dead tissue may be clear and intuitive, however, “visibly” dead tissue restoring to full recovery is still unclear. In this thesis, we search for potential answers to these raised questions from a novel dynamic modelling perspective that would fill in some of the missing gaps in the mechanisms of stroke evolution. We divided our thesis into five parts. In the first part, we give a clinical and imaging background on stroke and state the objectives of this thesis. In the second part, we summarize and review the literature in stroke and medical imaging. We specifically spot gaps in the literature mainly related to medical image analysis methods applied to acute-subacute ischemic stroke. We emphasize studies that progressed the field and point out what major problems remain. Noticeably, we have discovered that macroscopic (imaging-based) dynamic models that simulate how stroke lesion evolves in space and time were completely overlooked: an untapped potential that may alter and hone our understanding of stroke evolution. Progress in the dynamic simulation of stroke was absent –if not inexistent. In the third part, we answer this new call and apply a novel current-based dynamic model âpreviously applied to compare the evolution of facial characteristics between Chimpanzees and Bonobos [Durrleman 2010] – to ischemic stroke. This sets a robust numerical framework and provides us with mathematical tools to fill in the missing gaps between MR acquisition time points and estimate a four-dimensional evolution scenario of perfusion and diffusion lesion surfaces. We then detect two characteristics of patterns of abnormal tissue boundary change: spatial, describing the direction of change –outward as tissue boundary expands or inward as it contracts–; and kinetic, describing the intensity (norm) of the speed of contracting and expanding ischemic regions. Then, we compare intra- and inter-patients estimated patterns of change in diffusion and perfusion data. Nevertheless, topology change limits this approach: it cannot handle shapes with different parts that vary in number over time (eg: fragmented stroke lesions, especially in diffusion scans, which are common). In the fourth part, we suggest a new mathematical dynamic model to increase rigor in the imaging-based dynamic modeling field as a whole by overcoming the topology-change hurdle. Metamorphosis. It morphs one source image into a target one [Trouvé 2005]. In this manuscript, we extend it into dealing with more than two time-indexed images. We propose a novel extension of image-to-image metamorphosis into longitudinal metamorphosis for estimating an evolution scenario of both scattered and solitary ischemic lesions visible on serial MR. It is worth noting that the spatio-temporal metamorphosis we developed is a generic model that can be used to examine intensity and shape changes in time-series imaging and study different brain diseases or disorders. In the fifth part, we discuss our main findings and investigate future directions to explore to sharpen our understanding of ischemia evolution patterns.

Epileptic seizures are characterised by an onset of abnormal brain activity that evolves in space and time, which ultimately returns to normal background activity. For different types of seizures, the abnormal activity can be vastly different both in duration, electrographic morphology and spatial extent. Mechanistic understanding of the different seizure dynamics (spatially, as well as temporally) is crucial for the advancement and improvement of clinical treatment. To gain a deeper mechanistic insight into different seizure dynamics, mathematical models of brain processes were developed in this thesis. These models are used to explain electrographic seizure dynamics in their temporal, as well as their spatio-temporal evolution. Our studies show that the temporal evolution of seizure dynamics can be understood in terms of prototypic waveforms, which in turn can be represented in terms of three neural population processes. Such a minimal framework lends itself to a detailed phase space analysis, which elucidates seizure waveforms and seizure transitions as topological properties of the phase space. Based on the phase space considerations we show how during spike-wave seizures, single-pulse stimuli can have more complex effects than previously thought. In terms of the spatio-temporal dynamics of seizures, mechanisms for focal seizure onset and propagation are investigated in a model cortical sheet of coupled, discretised columns. The coupling followed nearest-neighbour, as well as realistic mesoscopic cortical connectivities. Different possible causes (e.g. spatial heterogeneities) of seizure generation, as well as different seizure spreading patterns (via different networks) have been investigated. We conclude that focal seizure onset can be due to global (e.g. whole-brain level) causes, global conditions & local triggers, and local (e.g. cortical column level) causes. Clinically relevant predictions from this work include the suggestion of a specific stimulation protocol in spike-wave seizures that incorporates phase space information; and the suggestion of using microscopic cortical incisions to disrupt the integrity of abnormal cortical tissue in order to prevent focal seizure onset. In conclusion, multi-scale computational modelling of seizure dynamics is proposed as an important tool to link theoretical understanding, experimental results, and patient-specific clinical data.

Depuis les années 1970, les pays du Pacifique sont de plus en plus fréquemment touchés par des maladies vectorielles telles que la Dengue, le Chikungunya ou le Zika. Le contrôle de ces maladies nécessite la connaissance de leur distribution spatio-temporelle au sein de la population ainsi que la compréhension des facteurs et mécanismes, souvent multiples, régissant cette distribution. Dans cette thèse, nous nous intéressons à la modélisation spatio-temporelle des déterminants de la dynamique spatiale de la dengue à l'échelle régionale du Pacifique, l'échelle territoriale de la Nouvelle-Calédonie, et l'échelle d'une ville, Nouméa, capitale de la Nouvelle-Calédonie.Dans le Pacifique, la dengue survient sous la forme de vagues épidémiques successives dues à l'introduction et à la diffusion régionale d'un nouveau sérotype tous les cinq à sept ans. En Nouvelle-Calédonie, la dengue présente une dynamique épidémique saisonnière, le sérotype dominant étant celui circulant dans la région. L'émergence d'une épidémie nécessite des conditions climatiques précises, et un indicateur annuel prédictif du risque d'émergence est maintenant utilisé de manière opérationnelle par les autorités de santé. Sur le plan spatial, au cours d'une épidémie, en moyenne, la circulation du virus est plus intense dans les zones où la température moyenne ainsi que les densités locales de population sont élevées. Que ce soit sur le territoire entier ou dans la ville de Nouméa, lors de la ré-émergence d'un même sérotype, la diffusion spatiale du virus paraît limitée par l'immunité de population créée par les épidémies précédentes. Cette thèse permet de mettre en évidence la nature complexe et multi-factorielle des maladies vectorielles, et de souligner l'intérêt d'analyses multi-échelles pour l'étude de leur épidémiologie. Au-delà des résultats obtenus sur la dengue dans la région Pacifique, notre volonté était de développer un cadre méthodologique pour l'analyse spatio-temporelle des données de surveillance épidémiologique applicable à d'autres contextes géographiques ou épidémiologiques. / Since the 1970's, the frequency of vector-borne diseases such as Dengue, Chikungunya or Zika has significantly increased in the Pacific region. Understanding the factors and mechanisms underlying the spatio-temporal distribution of these diseases provides useful information regarding their control and prevention. In this thesis, we identified dengue spatio-temporal patterns and used modeling tools to identify the factors associated to an increased epidemiological risk at a regional scale (Pacific), a territorial scale (New-Caledonia), and a city scale (Noumea, the capital of New-Caledonia).Every five to seven years, dengue spreads over the entire Pacific as large epidemics caused by the introduction and regional diffusion of one of the four dengue virus serotypes. In New Caledonia, dengue has a seasonal epidemic pattern. The emergence of an epidemic requires specific climatic conditions. The identification of these conditions led to the implementation of an operational early warning system to predict dengue annual epidemic risk. Spatially, at the territorial scale, during epidemic years, high levels of viral circulation are found in areas with higher mean temperature and higher local population densities. Whether at the territorial scale or at the city scale, the spatial diffusion of the virus during epidemics caused by the re-emergence of the same serotype seems limited by the population immunity created by past epidemics. This thesis highlights the complexity and the multi-factorial aspect of vector-borne diseases, and discusses the usefulness of a multi-scale approach in modelling their epidemiology. Besides enhancing our understanding of dengue epidemiology over the Pacific area, we also developed a methodological framework that can be used in other geographical or epidemiological settings for the spatio-temporal analysis and modeling of epidemiological surveillance data.

Cities have adopted evolving urban digitization strategies, and most of those increasingly focus on data, especially in the field of public transportation. Transportation data have intuitively spatial and temporal characteristics, for they are often described with when and where the trips occur. Since a trip is often described with many attributes, the transportation data can be presented with a tensor, a container which can house data in $N$-dimensions. Unlike a traditional data frame, which only has column variables, tensor is intuitively more straightforward to explore spatio-temporal data-sets, which makes those attributes more easily interpreted. However, it requires unique techniques to extract useful and relatively correct information in attributes highly correlated with each other. This work presents a mixed model consisting of tensor decomposition combined with seasonal vector autoregression in time to find latent patterns within historical taxi data classified by types of taxis, pick-up and drop-off times of services in NYC, so that it can help predict the place and time where taxis are demanded. We validated the proposed approach using the experiment evaluation with real NYC tax data. The proposed method shows the best prediction among alternative models without geographical inference, and captures the daily patterns of taxi demands for business and entertainment needs.