Doctor of Philosophy / Department of Electrical and Computer Engineering / Caterina Scoglio / Vector-borne diseases not only cause devastating economic losses, they also significantly impact human health in terms of morbidity and mortality. From an economical and humane point of view, mitigation and control of vector-borne diseases are essential. Studying dynamics of vector-borne disease transmission is a challenging task because vector-borne diseases show complex dynamics impacted by a wide range of ecological factors. Understanding these factors is important for the development of mitigation and control strategies. Mathematical models have been commonly used to translate assumptions concerning biological (medical, demographical, behavioral, immunological) aspects into mathematics, linking biological processes of transmission and dynamics of infection at population level. Mathematical analysis translates results back into biology. Classical deterministic epidemic models do not consider spatial variation, assuming space is homogeneous. Spatial spread of vector-borne diseases observed many times highlights the necessity of incorporating spatial dynamics into mathematical models. Heterogeneous demography, geography, and ecology in various regions may result in different epidemiological characteristics. Network approach is commonly used to study spatial evolution of communicable diseases transmitted among connected populations. In this dissertation, the spread of vector-borne diseases in time and space, is studied to understand factors that contribute to disease evolution. Network-based models have been developed to capture different features of disease transmission in various environments. Network nodes represent geographical locations, and the weights represent the level of contact between regional pairings. Two competent vector populations, Aedes mosquitoes and Culex mosquitoes, and two host populations, cattle and humans were considered. The deterministic model was applied to the 2010 Rift Valley fever outbreak in three provinces of South Africa. Trends and timing of the outbreak in animals and humans were reproduced. The deterministic model with stochastic parameters was applied to hypothetical Rift Valley fever outbreak on a large network in Texas, the United States. The role of starting location and size of initial infection in Rift Valley fever virus spread were studied under various scenarios on a large-scale network. The reproduction number, defined as the number of secondary infections produced by one infected individual in a completely susceptible population, is typically considered an epidemic threshold of determining whether a disease can persist in a population. Extinction thresholds for corresponding Continuous-time Markov chain model is used to predict whether a disease can perish in a stochastic setting. The network level reproduction number for diseases vertically and horizontally transmitted among multiple species on heterogeneous networks was derived to predict whether a disease can invade the whole system in a deterministic setting. The complexity of computing the reproduction number is reduced because the expression of the reproduction number is the spectral radius of a matrix whose size is smaller than the original next generation matrix. The expression of the reproduction number may have a wide range of applications to many vector-borne diseases. Reproduction numbers can vary from below one to above one or from above one to below one by changing movement rates in different scenarios. The observations provide guidelines on executing movement bans in case of an epidemic. To compute the extinction threshold, corresponding Markov chain process is approximated near disease free equilibrium. The extinction threshold for Continuous-time Markov chain model was analytically connected to the reproduction number under some assumptions. Numerical simulation results agree with analytical results without assumptions, proposing a mathematical problem of proving the existence of the relationships in general. The distance of the extinction threshold were shown to be closer to one than the reproduction number. Consistent trends of probability of extinction varying with disease parameters observed through numerical simulations provide novel insights into disease mitigation, control, and elimination.

Ziel dieser Doktorarbeit ist ein mathematisches Modell zu entwickeln, um eine mögliche Ausbreitung des West-Nil-Virus (WNV) in Deutschland zu simulieren und zu bewerten. Das entwickelte Werkzeug soll auch auf eine weitere, durch Zecken übertragene Krankheit, dem Krim-Kongo-Hämorrhagischen Fieber (CCHFV) angewendet werden. Die durch den Klimawandel verursachte globalen Erwärmung unterstützt auch die Verbreitung und Entwicklung verschiedener Vektorpopulationen. Dabei hat eine Temperaturerhöhung einen positiven Einfluss auf den Lebenszyklus des Vektors und die Zunahme der Vektoraktivität. In dieser Arbeit haben wir ein Differentialgleichungsmodell (ODE) entwickelt, um den Einfluss eines regelmäßigen Eintrags von Infektionserregern auf die empfängliche Population unter Berücksichtigung des Temperatureinflusses zu verstehen. Als Ergebnis haben wir einen analytischen Ausdruck der Basisreproduktionszahl und deren Wechselwirkung mit der Temperatur gefunden. Eine Sensitivitätsanalyse zeigt, wie wichtig das Verhältnis der anfälligen Mücken zur lokalen Wirtspopulation ist. Als ein zentrales Ergebnis haben wir den zukünftigen Temperaturverlauf auf Basis der Modellergebnisse des IPCC in unser Modell integriert und Bedingungen gefunden, unter denen es zu einer dauerhaften Etablierung des West-Nil-Virus in Deutschland kommt. Darüber hinaus haben wir die entwickelten mathematischen Modelle verwendet, um verschiedene Szenarien zu untersuchen, unter denen sich CCHFV möglicherweise in einer naiven Population etablieren kann, und wir haben verschiedene Kontrollszenarien mathematisch abgeleitet, um die Belastung von einer Infektion durch Zecken zu bewältigen. / The objective of this thesis is to develop the necessary mathematical model to assess the potential spread of West Nile Virus (WNV) in Germany and employ the developed tool to analyse another tick-borne disease Crimean- Congo Hemorrhagic Fever (CCHFV). Given the backdrop of global warming and the climate change, increasing temperature has benefitted the vector population. The increase in the temperature has a positive influence in the life cycle of the vector and the increase in its activities. In this thesis, we have developed an Ordinary Differential Equation (ODE) model system to understand the influence of the periodic introduction of infectious agents into the local susceptible population while taking account of influence of temperature. As results, we have found an analytic expression of the basic reproduction number and its interplay with the temperature. The sensitivity analysis shows us the importance of the ratio between the susceptible mosquitoes to the local host population. As a central result we have extrapolated the temperature trend under different IPCC conditions and found the condition under which the circulation of West Nile Virus will be permanent in Germany. Furthermore, we have utilised the developed mathematical models to examine different scenarios under which CCHFV can potentially establish in a naive population along with we mathematically derived different control scenarios to manage the burden of tick infection.

La connectivité marine est le transfert de larves et/ou d'individus entre des habitats marins éloignés. Grâce à la connectivité, les populations marines éloignées peuvent faire face à la pression de l'habitat en s'appuyant sur le transfert qui vient des populations éloignées de la même espèce. Le transfert entre les populations éloignées dans l'océan est possible par le transport dû aux courants. Cependant, il est pas encore clair si le champ des courants détermine totalement la persistance des espèces marines ou si la démographie locale joue un rôle. Les mesures in situ de la connectivité sont extrêmement difficiles. Par conséquence, notre connaissance de la connectivité est déduite des simulations numériques de dispersion. Le but de cette thèse est de préciser si la persistance de la connaissance du champ des courants et d’étudier l'effet des paramétrisations numériques dans l'estimation de la connectivité. Premièrement, je compare la théorie des graphes et le modèle de métapopulation pour déterminer si les courants ont un rôle prédominant. Cela permet d'identifier quelles mesures de la théories des graphes identifient de manière fiable les sites reproductifs importants pour la persistance en s'appuyant sur la connaissance des seuls courants. Deuxièmement, j’étudie les avantages et les lacunes de différents schémas de fermeture de turbulence. Ceci permet de préciser quel schéma reproduit mieux l'activité de turbulence dans des modèles numériques. Troisièmement, j'étudie les mécanismes générateurs de turbulence aux limites du fond. Ceci permet de connaître le coefficient de traînée effectif dû aux flux sur la topographie brute et de mieux estimer les flux turbulents. / Marine connectivity is the transfer of larvae and/or individuals between distant marine habitats. Thanks to connectivity, distant marine population can face habitat pressure by relying on the transfer from distant populations of the same species. The transfer between distant populations in the ocean is made possible by the transport due to the currents. However, it is still not clear if the current field totally determines the persistence of the marine species or if the local demography plays a role. Crucially, in situ measurements of connectivity are extremely difficult. Therefore, our knowledge about connectivity is inferred from numerical dispersal simulations. The aim of this thesis is to clarify if we can deduce the persistence from the knowledge of the current field and to investigate the effect of numerical turbulence parameterizations in estimating connectivity. Firstly, I compare graph theory and metapopulation model to determine if currents have a predominant role. This allows to identify which graph theory measures reliably identifies reproductive sites important for persistence by relying on the knowledge of currents only. Secondly, I investigate the advantages and shortcomings of different turbulence closure models. This allows to clarify which TCS better reproduces turbulence activity in numerical models. Thirdly, I investigate generating mechanisms of bottom boundary turbulence. This allows to know the effective drag coefficient due to flow over rough topography and better estimate turbulent fluxes.

The study of landscape structure and configuration is firmly established as integral to the continued advancement of ecology. The configuration of resource patches can have far-reaching implications for biodiversity, metapopulation dynamics, community structure, and habitat quality. Human activities, such as forestry, agriculture, and residential construction alter patch configuration by breaking larger patches into smaller fragments. This frequently results in pronounced, unforeseen consequences for species. The fragmentation and shrinking of habitat patches can lead to changes in the environmental conditions within the remaining patches (e.g., degradation), prompting responses from local populations. These responses can, in turn, cause changes to the metapopulation structure on large spatial scale.<br>I examined the relationship between the degree of habitat fragmentation (edge density), and forewing lengths of the ebony jewelwing damselfly (Calopteryx maculata Beauvois, Odonata: Calopterygidae). I used correlated random walks to determine the biologically relevant landscape area over which forest fragmentation was calculated. Then, I used Moran’s I to determine the spatial scale of wing length response to fragmentation. I found that wing lengths increased with edge density. I also found that wing lengths were spatially autocorrelated at distances below 5 Km. These findings suggest that damselflies adapt to changes in forest fragmentation at a relatively small spatial scale.<br>Next, I assessed the slime mold Physarum polycephalum’s usefulness as a microcosm of dispersal in fragmented landscapes. Slime mold plasmodia were placed in dishes with oat patches of varying sizes and distances. The probability of each patch type being colonized first was compared to predictions of patch occupancy based on C. maculata. Patches that were nearer or larger were likely to be colonized before patches that were more distant, or smaller. Observed patch occupancy matched model predictions when only patch distance was varied, but not when patch size was varied. These results suggest that P. polycephalum has the potential to serve as a useful microcosm of dispersal in patchy landscapes. However, more testing is needed to develop the microcosm system. <br>Finally, a lesson plan was developed to teach high school students about the concepts of landscape ecology and connectivity. An emphasis was placed on using active learning techniques, which have been demonstrated to result in greater understanding than traditional lecture formats. The lesson plan incorporates an education boardgame, Humans & Habitats, that I developed to illustrate how the conflicting goals of resource managers impact habitat connectivity. It also incorporates a scientific inquiry activity that uses P. polycephalum to test predictions about the effect of altered connectivity. The lesson plan and materials will be available to members of the public, free of charge.<br><br>

Dans la première partie de cette thèse, nous avons mis en place un métamodèle de transmission du paludisme basé sur la modélisation compartimentale susceptible-infecté-résistant (SIR) et prenant en compte les flux de mobilité humaine entre différents villages du Centre Sénégal. Les stratégies d’intervention géographiquement ciblées, s’étaient avérées efficaces pour réduire l’incidence du paludisme aussi bien dans les zones d’intervention qu’à l’extérieur de ces zones. Cependant, des actions combinées ciblant à la fois le vecteur et l’hôte, coordonnées à large échelle sont nécessaires dans les régions et pays visant l’élimination du paludisme à court/moyen terme.Dans la deuxième partie nous avons évalué différentes méthodes d’estimation de la mobilité humaine en l’absence de données individuelles. Ces méthodes incluaient la traçabilité spatio-temporelle des téléphones mobiles ainsi que les modèles mathématiques de gravité et de radiation. Le transport de l’agent pathogène dans l’espace géographique, par la mobilité d’un sujet infecté est un déterminant majeur de la vitesse de propagation d’une épidémie. Nous avons introduit le modèle d’impédance qui minimise l’erreur quadratique moyen sur les estimations de mobilité, en particulier dans les contextes où les ensembles de population sont caractérisés par leurs tailles hétérogènes.Nous avons enfin élargi le cadre des hypothèses sous-jacentes à la calibration des modèles de gravité de la mobilité humaine. L’hypothèse d’une distribution avec excès de zéros a fourni un meilleur ajustement et une meilleure prédictibilité, comparée aux hypothèses classiques n’assumant pas un excès de zéros : Poisson, Quasipoisson. / In the first part of this thesis, we have developed a malaria transmission metamodel based on the susceptible-infected-resistant compartmental modeling framework (SIR) and taking into consideration human mobility flows between different villages in the Center of Senegal. Geographically targeted intervention strategies had been shown to be effective in reducing the incidence of malaria both within and outside of intervention areas. However, combined interventions targeting both vector and host, coordinated on a large scale are needed in regions and countries aiming to achieve malaria elimination in the short/medium term.In the second part we have evaluated different methods of estimating human mobility in the absence of real data. These methods included spatio-temporal traceability of mobile phones, mathematical models of gravity and radiation. The transport of the pathogen through the geographical space via the mobility of an infected subject is a major determinant of the spread of an epidemic. We introduced the impedance model that minimized the mean square error on mobility estimates, especially in contexts where population sets are characterized by their heterogeneous sizes.Finally, we have expanded the framework of assumptions underlying the calibration of the gravity models of human mobility. The hypothesis of a zero inflated distribution provided a better fit and a better predictability, compared to the classical approach not assuming an excess of zeros: Poisson, Quasipoisson.