There is a growing interest in the dynamics of the co-infection of these two diseases. In this thesis, firstly we focus on studying the effect of a distributed delay representing the incubation period for the malaria parasite in the mosquito vector to possibly reduce the initial transmission and prevalence of malaria. This model can be regarded as a generalization of SEI models (with a class for the latently infected mosquitoes) and SI models with a discrete delay for the incubation period in mosquitoes. We study the possibility of occurrence of backward bifurcation. We then extend these ideas to study a full model of HIV and malaria co-infection. To get further inside into the dynamics of the model, we use the geometric singular perturbation theory to couple the fast and slow models from the full model. Finally, since the governing models are very complex, they cannot be solved analytically and hence we develop and analyze a special class of numerical methods to solve them.

In this thesis, we study these models and design and analyze robust numerical methods to solve them. To proceed in this direction, first we study the sub-models and then the full model. The first sub-model describes the transmission dynamics of HIV that accounts for behavior change. The impact of HIV educational campaigns is also studied. Further, we explore the effects of behavior change and different responses of individuals to educational campaigns in a situation where individuals may not react immediately to these campaigns. This is done by considering a distributed time delay in the HIV sub-model. This leads to Hopf bifurcations around the endemic equilibria of the model. These bifurcations correspond to the existence of periodic solutions that oscillate around the equilibria at given thresholds. Further, we show how the delay can result in more HIV infections causing more increase in the HIV prevalence. Part of this study is then extended to study a co-infection model of HIV-TB. A thorough bifurcation analysis is carried out for this model. Robust numerical methods are then designed and analyzed for these models. Comparative numerical results are also provided for each model.

<p>The global impact of the converging dual epidemics of tuberculosis (TB) and human immunodeficiency virus (HIV) is one of the major public health challenges of our time, because in many countries, human immunodeficiency virus (HIV) and mycobacterium tuberculosis (TB) are among the leading causes of morbidity and mortality. It is found that infection with HIV increases the risk of reactivating latent TB infection, and HIV-infected individuals who acquire new TB infections have high rates of disease progression. Research has shown that these two diseases are enormous public health burden, and unfortunately, not much has been done in terms of modeling the dynamics of HIV-TB co-infection at a population level. In this thesis, we study these models and design and analyze robust numerical methods to solve them. To proceed in this direction, first we study the sub-models and then the full model. The first sub-model describes the transmission dynamics of HIV that accounts for behavior change. The impact of HIV educational campaigns is also studied. Further, we explore the effects of behavior change and different responses of individuals to educational campaigns in a situation where individuals may not react immediately to these campaigns. This is done by considering a distributed time delay in the HIV sub-model. This leads to Hopf bifurcations around the endemic equilibria of the model. These bifurcations correspond to the existence of periodic solutions that oscillate around the equilibria at given thresholds. Further, we show how the delay can result in more HIV infections causing more increase in the HIV prevalence. Part of this study is then extended to study a co-infection model of HIV-TB. A thorough bifurcation analysis is carried out for this model. Robust numerical methods are then designed and analyzed for these models.&nbsp / Comparative numerical results are also provided for each model.</p>

<p>The global impact of the converging dual epidemics of tuberculosis (TB) and human immunodeficiency virus (HIV) is one of the major public health challenges of our time, because in many countries, human immunodeficiency virus (HIV) and mycobacterium tuberculosis (TB) are among the leading causes of morbidity and mortality. It is found that infection with HIV increases the risk of reactivating latent TB infection, and HIV-infected individuals who acquire new TB infections have high rates of disease progression. Research has shown that these two diseases are enormous public health burden, and unfortunately, not much has been done in terms of modeling the dynamics of HIV-TB co-infection at a population level. In this thesis, we study these models and design and analyze robust numerical methods to solve them. To proceed in this direction, first we study the sub-models and then the full model. The first sub-model describes the transmission dynamics of HIV that accounts for behavior change. The impact of HIV educational campaigns is also studied. Further, we explore the effects of behavior change and different responses of individuals to educational campaigns in a situation where individuals may not react immediately to these campaigns. This is done by considering a distributed time delay in the HIV sub-model. This leads to Hopf bifurcations around the endemic equilibria of the model. These bifurcations correspond to the existence of periodic solutions that oscillate around the equilibria at given thresholds. Further, we show how the delay can result in more HIV infections causing more increase in the HIV prevalence. Part of this study is then extended to study a co-infection model of HIV-TB. A thorough bifurcation analysis is carried out for this model. Robust numerical methods are then designed and analyzed for these models.&nbsp / Comparative numerical results are also provided for each model.</p>

There is a growing interest in the dynamics of the co-infection of these two diseases. In this thesis, firstly we focus on studying the effect of a distributed delay representing the incubation period for the malaria parasite in the mosquito vector to possibly reduce the initial transmission and prevalence of malaria. This model can be regarded as a generalization of SEI models (with a class for the latently infected mosquitoes) and SI models with a discrete delay for the incubation period in mosquitoes. We study the possibility of occurrence of backward bifurcation. We then extend these ideas to study a full model of HIV and malaria co-infection. To get further inside into the dynamics of the model, we use the geometric singular perturbation theory to couple the fast and slow models from the full model. Finally, since the governing models are very complex, they cannot be solved analytically and hence we develop and analyze a special class of numerical methods to solve them.

In this thesis, we study these models and design and analyze robust numerical methods to solve them. To proceed in this direction, first we study the sub-models and then the full model. The first sub-model describes the transmission dynamics of HIV that accounts for behavior change. The impact of HIV educational campaigns is also studied. Further, we explore the effects of behavior change and different responses of individuals to educational campaigns in a situation where individuals may not react immediately to these campaigns. This is done by considering a distributed time delay in the HIV sub-model. This leads to Hopf bifurcations around the endemic equilibria of the model. These bifurcations correspond to the existence of periodic solutions that oscillate around the equilibria at given thresholds. Further, we show how the delay can result in more HIV infections causing more increase in the HIV prevalence. Part of this study is then extended to study a co-infection model of HIV-TB. A thorough bifurcation analysis is carried out for this model. Robust numerical methods are then designed and analyzed for these models. Comparative numerical results are also provided for each model.

Ces travaux ont été menés dans le cadre du projet européen FACETS-ITN. Nous avons contribué à la simulation de cellules corticales grâce à des données expérimentales d'électrophysiologie comme référence et d'un circuit intégré neuromorphique comme simulateur. Les propriétés intrinsèques temps réel de nos circuits neuromorphiques à base de modèles à conductance, autorisent une exploration détaillée des différents types de neurones. L'aspect analogique des circuits intégrés permet le développement d'un simulateur matériel temps réel à l'échelle du réseau. Le deuxième objectif de cette thèse est donc de contribuer au développement d'une plate-forme mixte - matérielle et logicielle - dédiée à la simulation de réseaux de neurones impulsionnels. / This work has been supported by the European FACETS-ITN project. Within the frameworkof this project, we contribute to the simulation of cortical cell types (employingexperimental electrophysiological data of these cells as references), using a specific VLSIneural circuit to simulate, at the single cell level, the models studied as references in theFACETS project. The real-time intrinsic properties of the neuromorphic circuits, whichprecisely compute neuron conductance-based models, will allow a systematic and detailedexploration of the models, while the physical and analog aspect of the simulations, as opposedthe software simulation aspect, will provide inputs for the development of the neuralhardware at the network level. The second goal of this thesis is to contribute to the designof a mixed hardware-software platform (PAX), specifically designed to simulate spikingneural networks. The tasks performed during this thesis project included: 1) the methodsused to obtain the appropriate parameter sets of the cortical neuron models that can beimplemented in our analog neuromimetic chip (the parameter extraction steps was validatedusing a bifurcation analysis that shows that the simplified HH model implementedin our silicon neuron shares the dynamics of the HH model); 2) the fully customizablefitting method, in voltage-clamp mode, to tune our neuromimetic integrated circuits usinga metaheuristic algorithm; 3) the contribution to the development of the PAX systemin terms of software tools and a VHDL driver interface for neuron configuration in theplatform. Finally, it also addresses the issue of synaptic tuning for future SNN simulation.

La striction diffuse et localisée sont des phénomènes précurseurs à la rupture ductile et représentent l'une des principales causes de rebut des pièces métalliques au cours de leur mise en forme. La mise en œuvre d'outils théoriques et numériques capables de prédire l'apparition de ces défauts s'avère nécessaire pour des raisons économiques et environnementales. Ces outils nécessitent en partie l'intégration d'un modèle de comportement adéquat permettant de reproduire les phénomènes physiques mis en jeu. Un tel modèle de comportement est ensuite couplé à un indicateur d'instabilité plastique offrant la possibilité de prédire de manière fiable les phénomènes de striction diffuse et localisée. Dans ce travail de thèse, nous avons considéré certains modèles d'endommagement micromécaniques basés sur l'approche de Gurson, et qui ont été couplés à différents critères d'instabilités plastiques reposant sur l'Analyse de Bifurcation. L'implantation numérique des modèles retenus a été réalisée dans le code de calcul par éléments finis Abaqus/Standard. En ce qui concerne les modèles d'endommagement, plusieurs schémas d'intégrations ont été testés afin d'analyser leur performance et leur robustesse lorsque le comportement présente un effet adoucissant. L'approche combinant le modèle de comportement et les critères de striction a été utilisée pour prédire les limites de formabilité en striction diffuse et localisée de plusieurs matériaux métalliques. Les résultats obtenus ont permis de dresser une hiérarchisation théorique et numérique des critères de striction utilisés. / Diffuse and localized necking are precursors to ductile fracture, and represent one of the main causes of metal parts rejection during forming operations. The implementation of theoretical and computational tools to predict the occurrence of these defects turns out to be necessary for economic and environmental reasons. These tools require in part the introduction of an appropriate behavior model in order to reproduce the physical phenomena involved during forming operations. Such a behavior model is then coupled to a plastic instability indicator providing the ability to reliably predict diffuse and localized necking. In the present work, we considered a micromechanical damage models based on Gurson's approach, which were coupled to different plastic instabilities criteria, based on Bifurcation Analysis. The numerical implementation of these models was carried within the implicit finite element code Abaqus/Standard. With regard to the damage models, several integration schemes were tested to analyze their performance and robustness when the behavior exhibits softening effect. The approach combining the Gurson's damage model and necking criteria has been applied for the prediction of formability limits of several metallic materials. The obtained results allowed establishing a theoretical and numerical classification between the necking criteria used in this work.

Philosophiae Doctor - PhD / There is a growing interest in the dynamics of the co-infection of these two diseases. In this thesis, firstly we focus on studying the effect of a distributed delay representing the incubation period for the malaria parasite in the mosquito vector to possibly reduce the initial transmission and prevalence of malaria. This model can be regarded as a generalization of SEI models (with a class for the latently infected mosquitoes) and SI models with a discrete delay for the incubation period in mosquitoes. We study the possibility of occurrence of backward bifurcation. We then extend these ideas to study a full model of HIV and malaria co-infection. To get further inside into the dynamics of the model, we use the geometric singular perturbation theory to couple the fast and slow models from the full model. Finally, since the governing models are very complex, they cannot be solved analytically and hence we develop and analyze a special class of numerical methods to solve them. / South Africa

Diplomová práce pojednává o teorii chaotických dynamických systémů, speciálně se pak zabývá Rösslerovým systémem. Kromě standardních výpočtů spojených s bifurkační analýzou se práce zaměřuje na problém stabilizace, konkrétně na stabilizaci rovnovážných bodů. Ke stabilizaci je využita základní metoda zpětnovazebního řízení s časovým zpožděním. Významnou část práce tvoří zavedení a implementace obecné metody pro hledání vhodné volby parametrů vedoucí k úspěšné stabiliaci. Dalším diskutovaným tématem je možnost synchronizace dvou Rösslerových systémů pomocí různých synchronizačních schémat.