Traumatic injuries lead to articular cartilage lesion formation and result in the development of osteoarthritis. Recent research suggests that the early stage of mechanical injuries involve cell death (apoptosis and necrosis) and inflammation. In this thesis, we focus on building mathematical models to investigate the biological mechanism involving chondrocyte death and inflammatory responses in the process of cartilage degeneration. Chapter 1 describes the structure of articular cartilage, the process of carti- lage degeneration, and reviews of existing mathematical models. Chapter 2 presents a delay-diffusion-reaction model of cartilage lesion formation under cyclic loading. Computational methods were used to simulate the impact of varying loading stresses and erythropoietin levels. The model is parameterized with experimental results, and is therefore clinically relevant. Due to numerical limitations using delay differential equations, a new model is presented using tools for population dynamics. Chapter 3 presents an age and space-structured model of articular cartilage lesion formation un- der a single blunt impact. Age structure is introduced to represent the time delay in cytokine synthesis and cell transition. Numerical simulations produce similar tempo- ral and spatial patterns to our experimental data. In chapter 4, we extend our model under the cyclic loading setting. Chapter 5 builds a spatio-temporal model adapted from the former models, and investigates the distribution of model parameters using experimental data and statistical methods. Chapter 6 concludes.

<div>Public health policies increasingly rely on complex models that need to approximate epidemics realistically and be consistent with the available data. Choosing appropriate simplifying assumptions is one of the critical challenges in disease modeling. In this thesis, we focus on some of these assumptions to show how they impact model outcomes. </div><div>In this thesis, an ODE model with a gamma-distributed infectious period is studied and compared with an exponentially distributed infectious period. We show that, for childhood diseases, isolating infected children is a possible mechanism causing oscillatory behavior in incidence. This is shown analytically by identifying a Hopf bifurcation with the isolation period as the bifurcation parameter. The threshold value for isolation to generate sustained oscillations from the model with gamma-distributed isolation period is much more realistic than the exponentially distributed model.</div><div><br></div><div>The consequences of not modeling the spectrum of clinical symptoms of the 2014 Ebola outbreak in Liberia include overestimating the basic reproduction number and effectiveness of control measures. The outcome of this model is compared with those of models with typical symptoms, excluding moderate ones. Our model captures the dynamics of the recent outbreak of Ebola in Liberia better, and the basic reproduction number is more consistent with the WHO response team's estimate. Additionally, the model with only typical symptoms overestimates the basic reproduction number and effectiveness of control measures and exaggerates changes in peak size attributable to interventions' timing.</div><div><br></div>

Mathematical models, that depict the dynamics of a cancer cell population growing out of the human body (in vitro) in unconstrained microenvironment conditions, are considered in this thesis. Cancer cells in vitro grow and divide much faster than cancer cells in the human body, therefore, the effects of various cancer treatments applied to them can be identified much faster. These cell populations, when not exposed to any cancer treatment, exhibit exponential growth that we refer to as the balanced exponential growth (BEG) state. This observation has led to several effective methods of estimating parameters that thereafter are not required to be determined experimentally. We present derivation of the age-structured model and its theoretical analysis of the existence of the solution. Furthermore, we have obtained the condition for BEG existence using the Perron-Frobenius theorem. A mathematical description of the cell-cycle control is shown for one-compartment and two-compartment populations, where a compartment refers to a cell population consisting of cells that exhibit similar kinetic properties. We have incorporated into our mathematical model the required growing/aging times in each phase of the cell cycle for the biological viability. Moreover, we have derived analytical formulae for vital parameters in cancer research, such as population doubling time, the average cell-cycle age, and the average removal age from all phases, which we argue is the average cell-cycle time of the population. An estimate of the average cell-cycle time is of a particular interest for biologists and clinicians, and for patient survival prognoses as it is considered that short cell-cycle times correlate with poor survival prognoses for patients. Applications of our mathematical model to experimental data have been shown. First, we have derived algebraic expressions to determine the population doubling time from single experimental observation as an alternative to empirically constructed growth curve. This result is applicable to various types of cancer cell lines. One option to extend this model would be to derive the cell cycle time from a single experimental measurement. Second, we have applied our mathematical model to interpret and derive dynamic-depicting parameters of five melanoma cell lines exposed to radiotherapy. The mathematical result suggests there are shortcomings in the experimental methods and provides an insight into the cancer cell population dynamics during post radiotherapy. Finally, a mathematical model depicting a theoretical cancer cell population that comprises two sub-populations with different kinetic properties is presented to describe the transition of a primary culture to a cell line cell population.

In this study, we consider the mechanism design problem for the optimal allocation of fishing quotas at different total allowable catch (TAC) levels. An age-structured fish population model is employed. Fishing technologies are embedded in the economic model as a key determinant. As a result, we showed that the quota allocation mechanism is important to minimize the impact of fishing on total fish biomass or achieve maximum sustainable yield (MSY). Moreover, we indicated technology-based optimality conditions for allocation of quotas at different TAC levels, which minimize the impact of fishing on total fish biomass or enable us to achieve MSY. Under the consideration that the fishermen fulfill their remaining quotas through capturing untargeted (less revenue-generating) fish after the targeted fish population is fully caught, the fix ratio of the catch of targeted fish to untargeted fish is not valid anymore. Concordantly, we indicated technology-based optimal quota levels, including the interior solutions. In the EU, TACs are distributed among states according to the principle of &lsquo / relative stability&rsquo / which prescribes that the fishing quotas should be allocated based on historical catches of the EU states. In this context, rather than allocating the quotas based on historical catches, our main suggestion is that the structure of the fishing industry should be considered for allocation of quotas to provide the sustainability of EU fisheries and achieve responsible and effective management of the fishing industry in the EU.

Orientador: Rubens Maciel Filho / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-08T18:46:56Z (GMT). No. of bitstreams: 1 Oliveira_PatriciaCandiotoMigliari_D.pdf: 1584587 bytes, checksum: 8622cb86aacfe987908422e98c40d2c8 (MD5) Previous issue date: 2007 / Resumo: O trabalho envolveu modelo estruturado adaptado de um modelo estruturado de crescimento para processo de fermentação contínua realizado em um bioreator do tipo torre com células imobilizadas para produção de etanol. O modelo estruturado utilizado inclui equações de balanço para as rotas metabólicas fermentativa e respiratória, assim como termos cinéticos para o efeito de inibição pelo etanol, substrato e saturação celular no pellet. Os parâmetros cinético do modelo estruturado foram otimizados através da metodologia desenvolvida por Rivera (2005) onde envolve a aplicação de Algoritmo Genético, Planejamento Fatorial Fracionário proposto por Plackett Burman (1946) e Algoritmo Quasy Newton. Os resultados obtidos na simulação do modelo utilizando os parâmetros otimizados por esta metodologia representou de forma efetiva o modelo. A otimização do processo teve inicio com a Análise de Superfície de Resposta, que consistiu em um planejamento fatorial em estrela de dois níveis (-1 e +1) com um ponto central. A metodologia por Superfície de Resposta mostrou-se uma ferramenta poderosa para otimização preliminar das variáveis operacionais no sentido de que seus resultados foram usados como estimativas iniciais para o procedimento formal de otimização, SQP (Programação Quadrática Sucessiva). Esta metodologia de Superfície de resposta possibilita visualização do comportamento das variáveis que se quer otimizar, identificando a região do ponto ótimo, o que não é possível pelo método SQP. A metodologia SQP foi implementada com sucesso no modelo determinístico, obtendo as melhores condições de operação para as variáveis manipuláveis / Abstract: The work involved adapted of a structured model of growth structured model for process of continuous fermentation accomplished in a bioreator of the type tower with immobilized cells for etanol production. The used structured model includes reaction rate equations for the respiratory and glicolitic metabolic pathways, as well as kinetic terms for the inhibition effect for the etanol, substrate and cellular saturation in the pellet. The kinetic of the structured model parameters went optimized through to methodology developed by Rivera (2005) where it involves the application of Genetic Algorithm, methodology of Plackett¿Burman (1946) and Algorithm Quasi Newton. The results obtained in the simulation of the model using the parameters optimized for this methodology represented in an effective way the model. The optimization of the process had I begin with the Analysis of Surface of Answer, that consisted of a planning fatorial in star of two levels (-1 and +1) with a central point. The methodology for Surface of Answer a powerful tool was shown for preliminary optimization of the operational variables in the sense that its results were used as initial estimates for the formal procedure of optimization, SQP. This methodology of answer Surface facilitates visualization of the behavior of the variables that if that otimizar, identifying the area of the great point, what is not possible for the method SQP. The methodology SQP was implemented with success in the model deterministic, obtaining the best operation conditions for the variables manipulated. / Doutorado / Desenvolvimento de Processos Químicos / Doutor em Engenharia Química

Orientador: Rubens Maciel Filho / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-11T04:05:50Z (GMT). No. of bitstreams: 1 Lunelli_BetaniaHoss_D.pdf: 3246538 bytes, checksum: 66490737479c3e4a908963c18fd48b3c (MD5) Previous issue date: 2007 / Resumo: A síntese de ácido acrílico via processo fermentativo é um assunto recente, com poucas informações disponíveis na literatura e, tem despertado cada vez mais interesse de pesquisadores. Através da modelagem matemática, é possível obter uma melhor compreensão de um processo em sua totalidade, através de analogias abstratas que possibilitam a predição de um fenômeno. O objetivo deste trabalho consiste no desenvolvimento de modelos determinísticos para representar o processo biotecnológico de síntese de ácido acrílico a partir de uma rota metabólica alternativa, visando estudos do comportamento estacionário/dinâmico do processo, aplicação de técnicas de planejamento experimental para identificação dos parâmetros mais relevantes e otimização dos parâmetros operacionais, com a finalidade de compreender o processo e apresentar uma metodologia alternativa para a sua produção. A partir dos modelos desenvolvidos foi possível obter perfis de concentração dos principais componentes do processo. Depois de identificadas as influências dos parâmetros operacionais, cinéticos e de projeto sobre o processo, os parâmetros operacionais de cada modelo foram otimizados através da aplicação da metodologia de superfície de resposta e do método de otimização por programação quadrática sucessiva. Com a otimização dos parâmetros foi possível encontrar condições de operação que aumentaram a concentração e o rendimento final de ácido acrílico, como também, perceber as limitações dos métodos de otimização usados. Nos modelos com cinética estruturada foram aplicadas estratégias de controle, através das quais foi possível encontrar condições ótimas, podendo com isso operar o biorreator de forma eficiente e segura, além de aumentar o rendimento final de ácido acrílico. Através da realização deste trabalho, pode-se concluir que os modelos desenvolvidos constituem um conjunto de ferramentas interessantes para predizer e investigar o comportamento do processo de síntese de ácido acrílico via processo fermentativo, uma vez que, a literatura ainda não dispõe de trabalhos de modelagem para a síntese de ácido acrílico via rotas fermentativas. Também, servir de apoio para estudos de manipulação genética visando obter microrganismos com capacidade de produzir ácido acrílico em condições economicamente competitivas / Abstract: The acrylic acid synthesis by fermentative process is a recent subject, with few available information in literature and it has demonstrated each time more interest of researchers. Through the mathematical modeling, it is possible to obtain a better understanding of the process behavior if mechanistic models are developed. The purpose of this work is the deterministic model development for the biotechnological process of acrylic acid synthesis through an alternative metabolic route, aiming the studies of both the steady state and dynamic behavior of the process. To investigate the parameters interactions as well as to identify the parameters with the most significant impact on the model experimental design was used and operational parameters were optimized. The purpose is to understand the process and to present an alternative methodology for its production. From of the developed models was possible to obtain the concentration profiles of the process components main. After identified the influence of the operational, kinetic and design parameters about the process, the operational parameters were optimized through the application of the response surface methodology and the successive quadratic programming optimization method. With the optimization of parameters was possible to find out the optimal operational conditions and thus to increase the yield and acrylic acid concentration as well as to perceive the limitation of optimization methods used. In the models with structured kinetic were applied control strategies, where was possible to operate the bioreactor safe and efficiently as well as to increase the acrylic acid final yield. With the realization of this work, it follows that the models developed consist of a set of interesting tools to predict and investigate the behavior of the acrylic acid synthesis by fermentative process, whereas in the literature are not yet available works about modeling of the acrylic acid synthesis from fermentative routes, as well as can to serve as support for studies of genetic manipulation aiming at to obtain microorganisms with capacity to produce acrylic acid in competitive economically conditions / Doutorado / Desenvolvimento de Processos Químicos / Doutor em Engenharia Química

We study a scalable approach to information fusion for large sensor networks. The algorithm, field inversion by consensus and compressed sensing (FICCS), is a distributed method for detection, localization, and estimation of a propagating field generated by an unknown number of point sources. The approach combines results in the areas of distributed average consensus and compressed sensing to form low dimensional linear projections of all sensor readings throughout the network, allowing each node to reconstruct a global estimate of the field. Compressed sensing is applied to continuous source localization by quantizing the potential locations of sources, transforming the model of sensor observations to a finite discretized linear model. We study the effects of structured modeling errors induced by spatial quantization and the robustness of ℓ1 penalty methods for field inversion. We develop a perturbations method to analyze the effects of spatial quantization error in compressed sensing and provide a model-robust version of noise-aware basis pursuit with an upperbound on the sparse reconstruction error. Numerical simulations illustrate system design considerations by measuring the performance of decentralized field reconstruction, detection performance of point phenomena, comparing trade-offs of quantization parameters, and studying various sparse estimators. The method is extended to time-varying systems using a recursive sparse estimator that incorporates priors into ℓ1 penalized least squares. This thesis presents the advantages of inter-sensor measurement mixing as a means of efficiently spreading information throughout a network, while identifying sparse estimation as an enabling technology for scalable distributed field reconstruction systems.

Dans cette thèse on s'intéresse à un modèle mathématique décrivant l'adaptation du développement des populations de moustiques face à l'usage intensif des insecticides durant la nuit (moustiquaires imprégnées, répulsifs en spray, répulsifs avec diffuseur électrique, ...).Le modèle proposé dans cette thèse est structuré en âge et dépend du temps/moment où le moustique pique pour prendre son repas. Ceci nous conduità des modèles du type ultra parabolique. Le terme de renouvellement de lapopulation de moustiques est non-local, comme pour tous les problèmes démographiques, mais comporte ici un noyau qui permet à la nouvelle générationd'adapter son temps de piqure (repas). Ceci est dû à la sélection de certainsmoustiques qui piquent plus tôt ou plus tard que les autres moustiques, suite àla pression imposée par l'usage intensif des pesticides à l'intérieur des habitats et en particulier durant la nuit. Les conditions aux bords par rapport au moment de piqure (repas) seront périodiques car selon les espèces, les moustiques prennent toujours leurs repas au même moment de la journée.Les principaux résultats peuvent être classés dans 4 parties.Dans la première partie on présente un modèle structuré en âge décrivant laplasticité du moustique dans un environnement non contrôlé. On montre quele problème est bien posé via la théorie des semi-groupes. Le comportementasymptotique est décrit grâce à l'étude du spectre de l'opérateur A générateurdu C0 semi-groupe. On prouve également l'existence ou la non existence dessolutions stationnaires (sous certaines hypothèses).Dans la deuxième partie on s'intéresse à un problème de contrôle optimalde la population de moustiques. Le contrôle correspond à la proportion demoustiques éliminée et dépend du temps, de l'âge des moustiques et du tempsoù le moustique pique pour se nourrir. On démontre d’abord l’existence desolutions grâce à un argument de point fixe puis on établit des résultats decomparaisons pour notre problème. On établit ensuite l'existence d'un contrôleoptimal puis on dérive le système d'optimalité.Dans la troisième partie on s'intéresse à la question de contrôlabilité exacte locale pour le problème décrivant la capacité des moustiques à adapter leurdynamique face à l'usage intensif des insecticides. On établit une nouvelleinégalité de type Carleman pour le modèle structuré en âge avec diffusionet une condition au bord de renouvellement non-locale et des conditions auxbords périodiques par rapport au temps de piqure des moustiques.Dans la quatrième partie on s'intéresse au comportement en temps longd'un modèle non linéaire décrivant l'adaptation de la population des moustiques à l'usage intensif des insecticides. Quand le contrôle est petit (usage limité des insecticides) alors la population mature de moustiques devient grandeavec le temps et quand le contrôle est grand (usage intensif des insecticides)la population mature de moustiques devient petite avec le temps. Dans le casintermédiaire on obtient un modèle avec retard en temps pour la populationmature de moustiques qui peut être gouvernée par une sur-équation et unesous-équation. Finalement on montre que la sous-équation admet des ondesvoyageuses et la population mature de moustiques sera donc comprise entreces ondes voyageuses et les sur-solutions. / This dissertation is concerned with an age structured problem modelling mosquito plasticity. The main results can be divided into four parts.The first part presents an age structured problem modelling mosquito plasticity in a natural environment. We first investigate the analytical asymptotic solution through studying the spectrum of an operator A which is the infinitesimal generator of a C0-semigroup. Additionally, we get the existence and nonexistence of nonnegative steady solutions under some conditions.In the second part, we study the optimal control of an age structured problem. Firstly, we prove the existence of solutions and the comparison principle for a generalized system. Then, we prove the existence of the optimal control for the best harvesting. Finally, we establish necessary optimality conditions.In the third part, we investigate the local exact controllability of an age structured problem modelling the ability of malaria vectors to shift their biting time to avoid the stressful environmental conditions generated by the use of indoor residual spraying (IRs) and insecticide-treated nets (ITNs). We establish a new Carleman's inequality for our age diffusive model with non local birth processus and periodic biting-time boundary conditions.In the fourth part, we model a mosquito plasticity problem and investigate the large time behavior of matured population under different control strategies. Firstly, we prove that when the control is small, then the matured population will become large for large time and when the control is large, then the matured population will become small for large time. In the intermediate case, we derive a time-delayed model for the matured population which can be governed by a sub-equation and a super-equation. Finally, we prove the existence of traveling fronts for the sub-equation and use it to prove that the matured population will finally be between the positive states of the sub-equation and super-equation.

Dans cette thèse nous étudions l'influence de l'environnement sur le comportement d'une cellule dans deux situations différentes. Dans chacune de ces deux situations, apparaît un couplage non-linéaire sur le champ d'advection lié à un terme non-local provenant du bord du domaine. Dans une première partie, nous modélisons la polarisation cellulaire durant la conjugaison de la cellule de levure. Nous utilisons un modèle de type convection-diffusion avec un terme de convection non-linéaire et non-local. Ce modèle présente des similarités avec le modèle de Keller-Segel, la source du potentiel attractif étant sur le bord du domaine. Nous étudions le cas de la dimension un en utilisant des inégalités de Sobolev logarithmiques et HWI. En nous appuyant sur un raisonnement heuristique, nous ramenons l'étude de notre modèle en dimension deux au bord du domaine. Nous validons le modèle à l'aide des résultats expérimentaux obtenus par M. Piel en utilisant un bruit dynamique dans nos simulations numériques. Nous étudions ensuite le problème du dialogue cellulaire entre cellules de levure de sexe opposé. Dans une seconde partie, nous étudions la réaction immunitaire durant l'athérosclérose. Nous construisons puis développons un modèle structuré en âge pour décrire l'inflammation. Pour des paramètres particuliers, nous déterminons le comportement en temps long de notre système en utilisant une fonctionnelle de Lyapunov. / We investigate the influence of the environment on the behaviour of a cell in two different situations. In each of these situations, there is a non-linear coupling of the drift due to a non-local term coming from the boundary of the domain.The first part focuses on the modeling of cell polarisation during the mating of yeast. We use a convection-diffusion model with a non-linear and non-local drift. This model is similar to the Keller-Segel model, the source of the attractive potential comes from the boundary of the domain. We study the long time behaviour of the one-dimensional case by using logarithmic Sobolev and HWI inequalities.By relying on a heuristic, we reduce the study of our model in the two-dimensional case to the boundary of the domain. We validate the model with data provided by M. Piel. This validation requires adding a dynamical noise in our numerical simulations. We study then the cell discussion between yeast of opposite gender. In the second part we study the immune response in atherosclerosis. We build and then develop an age structured model in order to describe the inflammation. For specific parameters, we investigate the long time behaviour of our system by using a Lyapunov functional.

Ce mémoire concerne la modélisation mathématique de l’érythropoïèse, à savoir le processus de production des érythrocytes (ou globules rouges) et sa régulation par l’érythropoïétine, une hormone de contrôle. Nous proposons une extension d’un modèle d’érythropoïèse tenant compte du vieillissement des cellules matures. D’abord, nous considérons un modèle structuré en maturité avec condition limite mouvante, dont la dynamique est capturée par des équations d’advection. Biologiquement, la condition limite mouvante signifie que la durée de vie maximale varie afin qu’il y ait toujours un flux constant de cellules éliminées. Par la suite, des hypothèses sur la biologie sont introduites pour simplifier ce modèle et le ramener à un système de trois équations différentielles à retard pour la population totale, la concentration d’hormones ainsi que la durée de vie maximale. Un système alternatif composé de deux équations avec deux retards constants est obtenu en supposant que la durée de vie maximale soit fixe. Enfin, un nouveau modèle est introduit, lequel comporte un taux de mortalité augmentant exponentiellement en fonction du niveau de maturité des érythrocytes. Une analyse de stabilité linéaire permet de détecter des bifurcations de Hopf simple et double émergeant des variations du gain dans la boucle de feedback et de paramètres associés à la fonction de survie. Des simulations numériques suggèrent aussi une perte de stabilité causée par des interactions entre deux modes linéaires et l’existence d’un tore de dimension deux dans l’espace de phase autour de la solution stationnaire. / This thesis addresses erythropoiesis mathematical modeling, which is the process of erythrocytes production and its regulation by erythropeitin. We propose an erythropoiesis model extension which includes aging of mature cells. First, we consider an age-structured model with moving boundary condition, whose dynamics are represented by advection equations. Biologically, the moving boundary condition means that the maximal lifespan varies to account for a constant degraded cells flux. Then, hypotheses are introduced to simplify and transform the model into a system of three delay differential equations for the total population, the hormone concentration and the maximal lifespan. An alternative model composed of two equations with two constant delays is obtained by supposing that the maximal lifespan is constant. Finally, a new model is introduced, which includes an exponential death rate depending on erythrocytes maturity level. A linear stability analysis allows to detect simple and double Hopf bifurcations emerging from variations of the gain in the feedback loop and from parameters associated to the survival function. Numerical simulations also suggest a loss of stability caused by interactions between two linear modes and the existence of a two dimensional torus in the phase space close to the stationary solution.