A oxcarbazepina (OXC) é indicada como terapia adjuvante ou monoterapia no tratamento de crises epilépticas parciais ou crises tônico-clônicas generalizadas em adultos e crianças. A OXC sofre rápida eliminação pré-sistêmica com formação do metabólito ativo 10-hidroxicarbazepina (MHD), o qual possui como enantiômeros o R-(-)- e o S-(+)-MHD. A OXC e o MHD são substratos da glicoproteína-P (P-gp), que pode ser inibida pelo verapamil. O presente estudo avalia a influência do verapamil na farmacocinética e perfusão cerebral da OXC e dos enantiômeros do MHD em voluntários sadios. Os voluntários sadios (n=12) receberam em uma ocasião doses de 300 mg/12h de OXC e em outra ocasião doses de 300 mg/12h de OXC associadas com 80 mg/8h de verapamil. As amostras de sangue foram coletadas no estado de equilíbrio durante 12 horas e a avaliação da perfusão cerebral realizada utilizando a tomografia computadorizada por emissão de fóton único (SPECT) antes do início do tratamento e nos tempos 4, 6 ou 12h após a administração da OXC. As concentrações plasmáticas total e livre da OXC e dos enantiômeros do MHD foram avaliadas por LC-MS/MS. A análise farmacocinética não compartimental foi realizada com o programa WinNonlin e a farmacocinética populacional foi desenvolvida utilizando a modelagem não-linear de efeitos mistos com o programa NONMEM. Os limites de quantificação obtidos foram de 12,5 ng OXC/mL de plasma e 31,25 ng de cada enantiômero MHD/mL de plasma para a análise da concentração total, enquanto foi de 4,0 ng de OXC/mL de plasma e de 20,0 ng de cada enantiômero do MHD/mL de plasma para a determinação da concentração livre. Os coeficientes de variação obtidos nos estudos de precisão e a porcentagem de inexatidão inter e intra-ensaios foram inferiores a 15%, assegurando a reprodutibilidade e repetibilidade dos resultados. A análise farmacocinética não compartimental da OXC em monoterapia resultou nos seguintes parâmetros: concentração plasmática máxima (Cmax) de 1,35 ?g/mL como valor total e 0,32 ?g/mL como concentração livre em 1,0 h, área sob a curva concentração plasmática versus tempo (AUC0-12) de 3,98 ?g.h/mL e meia-vida de eliminação de 2,45 h, volume de distribuição aparente (Vss/F) de 352,17 L e clearance aparente (CLss/F) de 75,58 L/h. A disposição cinética do MHD é enantiosseletiva, com observação de maior proporção para o enantiômero S-(+)-MHD em relação ao R-(-)-MHD (razão AUC0-12 S-(+)/R-(-) de 4,26). A fração livre avaliada no tmax da OXC foi 0,26 para a OXC, 0,42 para o R-(-)-MHD e 0,38 para o S- (+)-MHD, mostrando enantiosseletividade na ligação às proteínas plasmáticas do MHD. O tratamento com o verapamil reduziu o tempo médio de residência (MRT) (4,71 vs 3,83 h) e Cmax como concentração livre (0,32 vs 0,53 ?g/mL) da OXC e aumentou os valores para ambos os enantiômeros do MHD de Cmax como valor total (2,60 vs 3,27 ?g/mL para o R-(-)- e 11,05 vs 11,94 ?g/mL para o S-(+)-MHD), Cmax como concentração livre (3,11 vs 4,14 ?g/mL para o S-(+)-MHD), Cmédia (2,11 vs 2,42 ?g/mL para o R-(-)- e 8,10 vs 9,07 ?g/mL para o S-(+)-MHD) e AUC0-12 (25,36 vs 29,06 ?g.h/mL para o R-(-)- e 97,19 vs 111,37 ?g.h/mL para o S-(+)-MHD). A ii farmacocinética populacional da OXC foi melhor descrita por modelo de dois compartimentos com eliminação de primeira ordem e com um conjunto de três compartimentos de trânsito para descrever o perfil de absorção da OXC. A disposição de ambos os enantiômeros do MHD foi caracterizada por modelo de um compartimento. Os valores de CLss/F estimados na monoterapia foram de 84,9 L/h para a OXC e de 2,0 L/h para ambos enantiômeros do MHD, enquanto os valores de Vss/F foram de 587 L para a OXC, 23,6 L para o R-(-)-MHD e 31,7 L para o S-(+)- MHD. Concluindo, a associação do verapamil aumentou a biodisponibilidade da OXC em 12% (farmacocinética populacional) e aumentou os valores de AUC de ambos os enantiômeros do metabólito MHD (farmacocinética não compartimental), o que está provavelmente relacionado com a inibição da P-gp no trato intestinal. A associação do verapamil aumentou as concentrações cerebrais preditas de ambos os enantiômeros do MHD em maior extensão do que aquelas observadas no plasma. As mudanças no fluxo sanguíneo cerebral (SPECTs realizados 6h após a administração da OXC) associadas à coadministração de verapamil provavelmente foram causadas pelo aumento dos níveis cerebrais de ambos os enantiômeros do MHD. A confirmação dessa observação requer um braço experimental adicional com SPECTs realizados também após a administração do verapamil em monoterapia. / Oxcarbazepine (OXC) is indicated as adjunctive therapy or monotherapy for the treatment of partial or generalized tonic-clonic seizures in adults and children. OXC undergoes rapid pre-systemic reduction with formation of the active metabolite 10- hydroxycarbazepine (MHD), which has the enantiomers R-(-)- and S-(+)-MHD. OXC and MHD are substrates of P-glycoprotein (P-gp), which can be inhibited by verapamil. The present study evaluates the influence of verapamil on the pharmacokinetics and cerebral perfusion of OXC and the MHD enantiomers in healthy volunteers. The healthy volunteers (n=12) received on one occasion doses of 300 mg/12h OXC and on another occasion they received doses of 300 mg/12h OXC associated with 80 mg/8h of verapamil. Blood samples were collected at steady state for 12 hours and the assessment of cerebral perfusion was performed using a single-photon emission computed tomography (SPECT) before the beginning of treatment and at times 4, 6 or 12 hours after OXC administration. The total and free plasma concentrations of OXC and MHD enantiomers were assessed by LC-MS/MS. The non-compartmental pharmacokinetics analysis was performed using the WinNonlin program, and population pharmacokinetics was developed using nonlinear mixed effects modelling with NONMEM.The limits of quantification obtained were 12.5 ng/mL plasma for OXC and 31.25 ng of each MHD enantiomer/mL plasma for total concentration analysis, while it was 4.0 ng OXC/mL plasma and 20.0 ng of each MHD enantiomer/mL plasma for the free concentration determination. The coefficients of variation obtained in studies of accuracy and the percentage of inaccuracy inter and intra-assay were less than 15%, ensuring the result reproducibility and repeatability. The non-compartmental pharmacokinetic analysis of OXC in monotherapy treatment, resulted in the following parameters: maximum plasma concentration (Cmax) of 1.35 ?g/mL as total concentration and 0.32 mg/mL as free concentration in 1.0 h, area under the plasma concentration vs time curve (AUC0-12) was 3.98 ?g.h/mL, half-life of 2.45 h, apparent volume of distribution (Vss/F) of 352.17 L and the apparent clearance (CLSS/F) of 75.58 L/h. The MHD kinetic disposition is enantioselective, with observation of a greater proportion of the S-(+)-MHD enantiomer compared to R-(-)-MHD (ratio AUC0-12 S-(+)/R-(-) of 4.26). The free fraction measured in the tmax of OXC was 0.26 for OXC, 0.42 for R-(-)-MHD and 0.38 for S-(+)-MHD, showing enantioselectivity in the plasma protein binding of MHD. Verapamil treatment reduced the mean residence time (MRT) (4.71 vs 3.83 h) and Cmax (0.26 vs 0.31 ?g/mL) as free concentration for OXC and increased the both MHD enantiomers values of Cmax (2.60 vs 3.27 ?g/mL for R-(-)- and 11.94 vs 11.05 ?g/mL for S-(+)-MHD) as total concentration, Cmax (3.11 vs 4,14 ?g/mL for S- (+)-MHD) as free concentration, Cavg (2.11 vs 2.42 ?g/mL for R-(-)- and 8.10 vs 9.07 ?g/mL for S-(+)-MHD) and AUC0-12 (25.36 vs 29.06 ?g.h/mL for R-(-)- and 97.19 vs 111.37 ?g.h/mL for S-(+)-MHD). The population pharmacokinetics of oxcarbazepine was best described by a two-compartment model with first-order elimination and a iv set of three transit compartments to describe the absorption profile of the parent compound. The disposition of both MHD enantiomers was characterised by onecompartment model. The CLss/F estimates in monotherapy were 84.9 L/h for OXC and 2.0 L/h for both MHD enantiomers, whereas the values of Vss/F were 587 L for OXC, 23.6 L for R-(-)-MHD and 31.7 L for S-(+)-MHD. In conclusion, verapamil coadministration increased the OXC bioavailability in 12% (population pharmacokinetics) and increased the AUC of both metabolite MHD enantiomers (non-compartmental pharmacokinetics), which is probably related to the inhibition of P-gp in the intestinal tract. Verapamil co-administration increased the predicted brain concentrations of both MHD enantiomers in a greater extent than those observed in plasma. Changes in cerebral blood flow (SPECTs performed 6h after administration of OXC) associated with co-administration of verapamil were probably caused by an increase in brain levels of both MHD enantiomers. Confirmation of this observation requires additional experimental arm with SPECTs also performed after administration of verapamil in monotherapy.

L’être humain est organisé selon une horloge interne d’une période d’environ 24 heures. La pharmacocinétique de certaines classes de médicaments est donc influencée par le rythme circadien. En effet, l’aire sous la courbe de la concentration en médicament en fonction du temps, la concentration maximale en médicament et le temps auquel on obtient la concentration maximale peuvent varier en fonction de l’heure à laquelle a été consommé le médicament. Le but de ce travail est de modéliser la variation de la concentration maximale de ces médicaments selon le moment de la journée auquel ils sont pris. On étudie d’abord un modèle présenté par Godfrey permettant de trouver la concen- tration en médicament en fonction du temps et tenant compte des variations circadiennes. Ce modèle ne permet pas d’illustrer les variations dans la concentration maximale selon le moment de la journée auquel le médicament est pris. Un nouveau modèle à deux com- partiments sera donc développé pour les trois modes d’absorption (orale, intraveineuse, intraveineuse bolus). Les systèmes d’équations différentielles résultants seront étudiés. L’effet de la variation des paramètres de phase sur la concentration maximale sera aussi étudié. La preuve de l’existence des solutions, de leur unicité et de leur positivité sera faite en annexe. / Humans are organised according to an internal clock with a period of approximatively 24 hours. The pharmacokinetic of several classes of drugs are then influenced by circadian rhythms. Indeed, the area under the curve (of the drug concentration as a function of time), the maximal concentration and the time to maximal concentration can change according to the time at which the drug is taken. The objective of this present work is to find a model to represent the variations in the maximal drug concentration according to the absorption’s time. We first study a model presented by Godfrey. It allows to find the drug concentration as a function of time while taking into account circadian rhythms. Unfortunately, this model could not represent the variations in the maximal concentration according to the time at which the drug is taken. We developed a new two-compartmental model for the three ways of absorption (oral, intravenous and intravenous bolus). The resulting systems of ordinary differential equations will be studied. The effect of the phase parameters on the maximal concen- tration will also be studied. Finally, the proof of well-poseness of the model will be developed in the Annex.

>Magister Scientiae - MSc / Herbal medicines have been an important part of health and wellness for hundreds of years. Recently the World Health Organization estimated that 80% of people worldwide rely on herbal medicines. Herbs contain many substances that are good for protecting the body and are therefore used in the treatment of various illnesses. Along with traditional medicines, herbs are often used in the treatment of chronic diseases such as rheumatism, migraine, chronic fatigue, asthma, eczema, and irritable bowel syndrome, among others. Herbal medicines are also applied in certain traditional communities as treatment against infectious diseases such as flu, malaria, measles, and even human immunodeficiency virus HIV-infection. Approximately 34 million people are currently infected with the human immunodeficiency virus (HIV) and 2.5 million newly infected. Therefore, HIV has become one of the major public health problems worldwide. It is important to understand the impact of herbal medicines used on HIV/AIDS. Mathematical models enable us to make predictions about the qualitative behaviour of disease outbreaks and evaluation of the impact of prevention or intervention strategies. In this dissertation we explore mathematical models for studying the effect of usage of herbal medicines on HIV. In particular we analyze a mathematical model for population dynamics of HIV/AIDS. The latter will include the impact of herbal medicines and traditional healing methods. The HIV model exhibits two steady states; a trivial steady state (HIV-infection free population) and a non-trivial steady state (persistence of HIV infection). We investigate the local asymptotic stability of the deterministic epidemic model and similar properties in terms of the basic reproduction number. Furthermore, we investigate for optimal control strategies. We study a stochastic version of the deterministic model by introducing white noise and show that this model has a unique global positive solution. We also study computationally the stochastic stability of the white noise perturbation model. Finally, qualitative results are illustrated by means of numerical simulations. Some articles from the literature that feature prominently in this dissertation are [14] of Cai et al, [10] of Bhunu et al., [86] of Van den Driessche and Watmough, [64] of Naresh et al., Through the study in this dissertation, we have prepared a research paper [1], jointly with the supervisors to be submitted for publication in an accredited journal. The author of this dissertation also contributed to the research paper [2], which close to completion. 1. Abdulaziz Y.A. Mukhtar, Peter J. Witbooi and Gail D. Hughes. A mathematical model for population dynamics of HIV with ARV and herbal medicine. 2. P.J. Witbooi, T. Seatlhodi, A.Y.A. Mukhtar, E. Mwambene. Mathematical modeling of HIV/AIDS with recruitment of infecteds.

Acute liver failure (ALF) is a rare but devastating clinical syndrome with multiple causes and a variable course. The mortality rate is high. Orthotopic liver transplantation is the only therapy of proven survival benefit but the limited supply of donor organs, the rapidity of progression and the variable course of ALF limit its use. A need therefore exists for a method to ‘bridge’ patients, that is, provide temporary support, to either the spontaneous regeneration of the innate liver or transplantation. One possibility includes bio-artificial liver support systems (BALSS). This technology is composed of an extracorporeal circulation system incorporating a bioreactor that contains parenchymal liver cells (hepatocytes) to perform the detoxifying, transforming and synthetic properties of a liver. However, the development of a BALSS holds particular challenges. Despite approximately four decades of research, bio-artificial liver (BAL) technology globally remains in a pre-commercial stage. The University of Pretoria (UP) and the Council for Scientific and Industrial Research (CSIR) have developed a BALSS with novel characteristics. These include a computationally optimized radial-flow primary porcine hepatocyte bioreactor perfused with blood plasma, and a perfluorocarbon oxygen carrier which replaces hemoglobin. There are also novel design properties in the circulation system itself. Demonstrating the metabolic and clinical efficacy of a BAL device requires implementing, in vitro (cell biology), in vivo (animal) and mathematical modeling studies. These studies are a formal necessity but are inherently ‘models’ of the in vivo human clinical circumstance. That is, they are limited by their experimentally controlled configuration/s. In investigating these, this thesis firstly provides a foundation by reviewing the clinical and biological context of ALF and BAL technology, then presents and evaluates particular studies/models that have been implemented over several years in the course of the UP-CSIR BAL project. For each section, thoughts and recommendations regarding future work that will facilitate the development of BAL technology are discussed in detail. The thesis is concluded with an evaluation of success and the consensus-agreed requirement of continued research and innovation in the field. / Thesis (PhD)--University of Pretoria, 2010. / Chemical Engineering / unrestricted

La dengue est une infection virale qui touche de 100 à 400 millions d'individus chaque année. Selon l'OMS, « la dengue sévère est l’une des principales maladies graves et causes de décès dans certains pays d’Asie et d’Amérique latine ». Il est justifiable de modéliser la propagation de cette maladie dans une population à l'aide de modèles mathématiques compartimentaux. Les travaux de Forshey et al. sur la fièvre dengue semblent indiquer la possibilité qu'une infection à la dengue ne donne pas une immunité à long terme contre les différents sérotypes du virus, et qu'une réinfection homotypique à la dengue serait commune. Nous étudions un modèle SIRS de la dengue qui prend en compte cette perte d'immunité via un système d'équations différentielles à délai. Nous caractérisons les états stationnaires et leur stabilité en termes des différents paramètres considérés, notamment les taux de reproduction de base associés à chacun des sérotypes de la dengue. Nous étudions les bifurcations du système en ses principaux paramètres, notamment les bifurcations de Hopf émergeant de la présence d'un délai dans le système d'équations différentielles. Des simulations numériques du modèle sont présentées afin de représenter les différents régimes du modèle à l'étude. / Dengue is a viral infection affecting from 100 to 400 million people each year. According to the WHO, "severe dengue is a leading cause of serious illness and death in some Asian and Latin American countries". This justifies the modelling of this illness's propagation in a population using mathematical compartmental models. Results of Forshey et al. on dengue fever seem to indicate the possibility that a dengue infection does not yield a long term immunity against the different dengue serotypes, and that an homotypical reinfection could be common. We study a SIRS model for the dengue virus that takes into account this loss of immunity via a system of delay differential equations. We characterize the stationary states and their stability in terms of the different parameters considered, in particular the basic reproduction ratios associated to each dengue serotype. We study the system's bifurcations in its main parameters, especially the Hopf bifurcations arising from the presence of a delay in the system of differential equations. Numerical simulations of the model are presented to represent the model's different regimes.

This work focuses on issues relating to the perfusion analysis. The aim of this work is to perform experimental measurements of the phantom and then evaluate the perfusion curves. This curves are used to himation of perfusion hemodynamic parameters, which indicates important informatik about monitoring area. All processes associated with the designation and evaluation are performed in a program named Matlab. The output of work is a system that provides the reader into the problem of perfusion analysis and allows him to understand and know what is the meaning od analysis, what demands are placed on the evaluation and what is the result of this perfusion analysis.

Infusion pumps are used in all departments of a hospital, in the emergency care unit as well as in pediatrics. The pumps administer intravenous medications for the purpose of helping patients to manage pain and are unfortunately not spared from emerging errors. Due to the complexity of the process involved in infusion pumps, errors regarding delay in administration are encountered. Especially vulnerable to errors are pediatric patients, due to the high risk of over- or under-dosing. This study aims to investigate the effects on administration delay by analysing the medical supply and system utilized for the infusion pumps. This is accomplished through implementation of Compartmental Modeling in Pharmacokinetics in combination with a self developed mathematical model for estimating the administration delay. Simulations were performed for analysing how various sizes of medical supply effected delay time. The result from the computed mathematical model indicates that increased volumes on utilized equipment will increase delay time. The combined use of a decreased flow rate and smaller equipment sizes will have the greatest affects on the delay in administration. The result obtained from the computed compartmental model can be useful for medical staff to be able to estimate the delay in administration. However, further validation is required before the utilization of the model can be applied in hospitals. / Infusionspumpar används på alla avdelningar på ett sjukhus, inom akutvården samt inom pediatrik. Pumparna administrerar olika mediciner i syfte att hjälpa patienten att hantera smärta och är tyvärr inte förskonade från att fel kan förekomma. På grund av komplexiteten i processen, involverad i infusionspumpar, uppstår fel gällande förseningar i administrering av medicin. Speciellt sårbara för dessa typer av förseninigar är pediatriska patienter, på grund av den förhöjda risker gällande över- eller underdosering. Denna studie syftar till att undersöka effekterna gällande administreringsfördröjning genom att analysera det medicinska utrustningen och systemet som används för infusionspumparna. Detta uppnås genom implementering av kompartmentmodellering i farmakokinetik i kombination med en egenutvecklad matematisk modell för att uppskatta administreringsfördröjningen. Simuleringar utfördes för att analysera effekterna av olika storlekar på medicinsk utrustning i förhållande till fördröjningen av administreringe. Resultatet från den beräknade matematiska modellen indikerar att ökade volymer gällande den medicinska utrustningen kommer att öka fördröjningstiden. Den kombinerade användningen av en minskad flödeshastighet och mindre utrustningsstorlekar kommer att ha störst inverkan på förseningen i administreringen. Resultatet som erhålls från den beräknade kompartmentmodellen kan vara användbar för sjukvårdspersonal för att kunna uppskatta förseningen i administrationen. Ytterligare validering krävs dock innan användningen av modellen kan tillämpas på sjukhus.

The goal of this research work was to understand the clinical-pharmacology based treatment approaches for sorafenib. Treatment with sorafenib is associated with high inter-patient variability in pharmacokinetic exposures, efficacy and toxicity. We explored the demographic, laboratory, clinical and pharmacogenetic factors to elucidate the sources of variability. In addition, we examined the impact of pharmacogenetic variation in VEGFR2, an important mediator of the VEGF pathway, on risk of prostate cancer. To support these investigations, (mainly single-dose) pharmacokinetic, pharmacogenetic, efficacy and toxicity information were collected from patients with solid tumors, enrolled in five phase I / II clinical trials at National Cancer Institute. Non-compartmental analysis-general linear modeling (NCA-GLM), population pharmacokinetic analysis and several correlative studies were performed to characterize the sources of variability in pharmacokinetics and response. The role of prostate specific antigen (PSA) and ex-vivo anti-angiogenic activity as efficacy markers was evaluated, respectively, for patients with prostate cancer treated with sorafenib and patients with solid tumors treated with combination of sorafenib and bevacizumab. Sweat concentrations of sorafenib were measured to study its association with development of hand-foot skin reaction (HFSR). Only body weight was a significant covariate for volume of distribution by population pharmacokinetic analysis, while BSA, albumin and UGT1A9*3 appeared to be significant by NCA-GLM. However, the contribution of these covariates in overall exposure variability was very small; hence, these were considered clinically irrelevant. The association of sorafenib exposure with efficacy in patients with prostate cancer, colorectal cancer and combined solid tumors were not significant; exposure-efficacy relationship for lung cancer patients requires further evaluation. Sorafenib exposures appeared to be associated with incidences of rash in single agent trials and with HFSR in trials involving treatment with sorafenib and bevacizumab combination. In-vitro cell-line experiments determined that prostate specific antigen (PSA) is not a suitable marker of efficacy in patients with prostate cancer treated with sorafenib. The ex-vivo anti-angiogenic activity, measured by rat-aortic ring assay using patient serum samples, appeared to be not associated with clinical response. Sorafenib concentration in sweat, upto ≥5 ng/mL, apparently was not associated with HFSR. The VEGFR2 H472Q polymorphism was associated with progression-free survival (PFS) (with an apparent heterozygous advantage for survival) and toxicities in patients treated with drugs against the VEGF pathway. Patients who developed hypertension and HFSR on bevacizumab and sorafenib therapy, respectively, appeared to have longer PFS. Therefore, these side effects should be effectively managed to avoid/delay the treatment discontinuation. The VEGFR2 H472Q and V297I genotype were not predictive of risk of prostate cancer in Caucasian subjects.

Les abondances relatives naturelles des différents isotopes stables de l'azote (δ15N) varient selon les tissus au sein d'un individu et selon les individus au sein d'une population, et ces différences reflètent à la fois les caractéristiques de structure et de fonctionnement du métabolisme azoté et ses modulations en lien avec des variations des conditions nutritionnelles et physio-pathologiques. Cette thèse vise, à travers une approche couplée d'expérimentation et de modélisation, à mieux caractériser et comprendre les modulations des δ15N des différents pools azotés et à démontrer la capacité des δ15N à fournir des informations sur les flux azotés de l'organisme, leurs valeurs et modulations, qui sont encore mal connus. Nous avons, dans un premier temps, mesuré les δ15N dans plusieurs tissus (intestin, foie, plasma, muscles, rein, peau...) et dans différentes fractions azotées (acides aminés, protéines, urée, NH4) chez le rat, dans différentes conditions nutritionnelles (chez des rats nourris avec des P de qualité différente, les protéines de lait et de soja) ou physiopathologiques (chez des rats présentant ou non un syndrome métabolique, associant insulino-résistance et obésité, après avoir consommé un même régime potentiellement obésogène). Ces données expérimentales nous ont permis (i) de montrer que l'écart de δ15N entre les protéines tissulaires et le régime est plus important lorsque la qualité protéique est moindre, et (ii) de mettre en évidence que, lors de l'initiation précoce d'un syndrome métabolique associant insulino-résistance et obésité, les δ15N de certains pools métaboliques sont modulés et constituent des signatures isotopiques des modulations métaboliques associées. Par ailleurs, grâce à l'analyse par modélisation compartimentale des cinétiques de δ15N mesurées expérimentalement dans les fractions acides aminés et protéines de différents tissus après augmentation du δ15N du régime, nous avons pu estimer les taux de renouvellement protéique tissulaires et explorer la structure et le fonctionnement des échanges entre acides aminés et protéines des différents tissus et comparer leur degré de compartimentation. Enfin, nous avons développé un modèle multi-compartimental reproduisant l'ensemble des flux azotés inter- et intra-organes de l'organisme et rendant compte des variations de δ15N observées. Cette représentation globale du métabolisme azoté fournit une vision novatrice du fonctionnement intégré du métabolisme azoté dont les données éparses de la littérature ne donnaient auparavant qu'une vision parcellaire et fragmentée. Le modèle a permis de reconstituer les mécanismes qui conduisent à l'observation de différences de δ15N entre pools azotés, de mieux comprendre quelles modulations sont les plus susceptibles d'affecter les δ15N, avec quelle amplitude et dans quel sens, et finalement d'expliquer les variations de δ15N mises en évidence expérimentalement en terme de modulation des flux azotés. L'ensemble de nos résultats d'expérimentation et de modélisation démontre la capacité des δ15N à apporter des informations sur les flux métaboliques azotés et souligne l'intérêt prometteur de cette approche nouvelle pour acquérir une compréhension intégrée du système complexe du métabolisme azoté inter- et intra-organes et des processus homéostatiques qui le régulent et de ses dérégulations pré-pathologiques. / Natural abundances of stable nitrogen isotopes vary among tissues within an individual and among individuals within a population, and these differences are linked to the structural and functioning characteristics of the nitrogen metabolism and also to its modulations in response to variations in nutritional and physiological conditions. In this thesis, we developed an approach combining both experimentation and modeling, in order to better characterize and understand the modulations in the δ15N values of various nitrogen metabolic pools, and to show the capacity of the δ15N to provide information regarding the values and modulations of the body nitrogen fluxes, that are still poorly determined. We first measured the δ15N in various tissues (intestine, liver, plasma, muscle, kidney, skin …) and in various nitrogen fractions (amino acids, proteins, urea, NH4) in rats, under different nutritional (i.e. in rats fed with P of distinct quality, that were milk and soy P) or pathophysiological (i.e. in rats that had or not become obese and insulin resistant after being fed a high-fat diet for 10 weeks). From these experimental data, we showed (i) that the tissue nitrogen discrimination (i.e., the difference between tissue and diet δ15N) is higher when the P is of lesser quality, and (ii) that, during the onset of a metabolic syndrome, in the presence of both insulin resistance and obesity, the δ15N differed in some nitrogen pools and thus constitute isotopic signatures of the metabolic impact of such conditions. In this thesis, we also measured the δ15N kinetics in the amino acid and protein fractions of several tissues after a shift in the diet δ15N. The analysis of these kinetics, using a compartimental modeling approach, enabled us to estimate tissue fractional turnover rates and to investigate the structure and the functioning of the protein synthesis and breakdown exchanges in some tissues and their level of compartmentation. Lastly, we developed a multi-compartmental model that describes the various body nitrogen transfers between and within tissues and accounts for the observed δ15N variability. This model of the nitrogen metabolism provides a new and systemic insight of the interactions and modulations of the various nitrogen fluxes, as opposed to the fragmented information available from the literature data. This model enabled us to reconstruct the mechanisms that caused the observed δ15N differences between nitrogen pools, to better understand how they vary, depending on which metabolic modulation and with which amplitude, and finally to hypothesize which nitrogen fluxes alterations are the more likely to be responsible for the δ15N variations that we observed in our experimentations. In conclusion, our experimental and modelling results show that it is feasible to gain information from the δ15N values regarding the metabolic nitrogen fluxes and their modulations, and highlight the interest of this new approach to get an integrated insight into the complex nitrogen metabolic system and a better understanding of the way the various between and within tissues nitrogen fluxes are regulated and altered.

>Magister Scientiae - MSc / In this thesis, we investigate the HIV/AIDS epidemic in a population which experiences a significant flow of immigrants. We derive and analyse a math- ematical model that describes the dynamics of HIV infection among the im- migrant youths and intervention that can minimize or prevent the spread of the disease in the population. In particular, we are interested in the effects of public-health education and of parental care.We consider existing models of public-health education in HIV/AIDS epidemi-ology, and provide some new insights on these. In this regard we focus atten-tion on the papers [b] and [c], expanding those researches by adding sensitivity analysis and optimal control problems with their solutions.Our main emphasis will be on the effect of parental care on HIV/AIDS epidemi-ology. In this regard we introduce a new model. Firstly, we analyse the model without parental care and investigate its stability and sensitivity behaviour.We conduct both qualitative and quantitative analyses. It is observed that in the absence of infected youths, disease-free equilibrium is achievable and is asymptotically stable. Further, we use optimal control methods to determine the necessary conditions for the optimality of intervention, and for disease eradication or control. Using Pontryagin’s Maximum Principle to check the effects of screening control and parental care on the spread of HIV/AIDS, we observe that parental care is more effective than screening control. However, the most efficient control strategy is in fact a combination of parental care and screening control. The results form the central theme of this thesis, and are included in the manuscript [a] which is now being reviewed for publication. Finally, numerical simulations are performed to illustrate the analytical results.