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El, Idrissi Omar. "Analysis of a prey-predator model in age-structured population dynamics." Doctoral thesis, Universitat Autònoma de Barcelona, 2001. http://hdl.handle.net/10803/3070.
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Heery, Eliza Crenshaw. "The impact of bias in length frequency data on an age structured fisheries stock assessment model." Thesis, Virginia Tech, 2007. http://hdl.handle.net/10919/32865.
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Statistical age-structured models are widely used in fisheries stock assessment. These models have been become increasingly complex over recent decades, allowing them to incorporate a larger variety of fisheries data. These typically include information regarding annual fishery yields, indices of abundance and catch composition data, which reflect the distribution of ages in the harvested population each year. In some fisheries, age composition can be determined annually through the examination of annuli on hard parts, such as otoliths or scales. These methods are, however, costly, time consuming and require a relatively high level of expertise on the part of data collectors. Alternatively, length frequency distributions within the annual catch are relatively simple and inexpensive to acquire, and can be employed to extrapolate age structure given that some information regarding age length relationships in the population is known. This type of data is therefore critical for many age-structured fisheries models.
Length frequency data are compiled from length measurements of a sub-sample of the commercial catch. Even when they derive from a relatively large sample size, however, these data depend on a number of biological, economic and logistical factors. In some fisheries, for example, larger, more valuable fish may be separated from the overall catch and sold quickly, before port samplers have chance to gather sub-samples (Burns et al. 1983). This can reduce the relative frequency of large individuals in length frequency data. Alternatively, fish may become stratified in holding bins or storage containers according to size, due to their slippery texture and body shape (Hilborn and Walters 1992). With smaller, shorter individuals falling to the bottom where they are less likely to be picked up and measured, length frequency data may contain a disproportionately high frequency of large fish.
This study used simulations to examine the impact of these two types of bias in length frequency data on a statistical age-structured model. The model, which was similar to those used in stock assessments for black sea bass (Centropristis striata) and gag (Mycteroperca microlepis) in the southeastern United States, produced erroneous population estimates when given biased data. Length frequency data that contained too many small fish caused stock status estimates to became overly pessimistic, indicating that populations were more heavily depleted than was actually the case. This type of bias supported overly conservative management measures, which posed an unnecessary cost to fishermen. Conversely, when the data included too many large fish, estimates of stock status were overly optimistic, and supported management actions that did not effectively protect the stock from overfishing. These results indicate that the quantity of length frequency data alone does not protect against bias when using complex age-structured models. The likelihood and magnitude of bias in these must also be examined in order to determine whether results are likely to be biased. For a given fishery, it is therefore critical that potential sources of bias in length frequency data be thoroughly inspected, and that the modeling approach used to assess the stock be appropriate based on the availability and accuracy of the data.Master of Science
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Kanik, Zafer. "Mechanism Design For The Optimal Allocation Of Quotas And The Determination Of The Total Allowable Catch For Eu Fisheries Under An Age-structured Model." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614678/index.pdf.
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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 &lsquorelative 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.
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Hutton, Trevor P. "The status and productivity of the Cape hake stock off the west coast of South Africa based on an age-structured production model with different stock-recruitment and fishing selectivity-at-age relationships." Master's thesis, University of Cape Town, 1993. http://hdl.handle.net/11427/21629.
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Bibliography: pages 41-47The surplus production model and ad hoc tuned VPA assessment methods currently used to provide the basis for scientific TAC recommendations for the Cape hake resource off South Africa provide rather different appraisals of the current status and productivity of this resource. The production model approach is based on the Butterworth-Andrew observation error estimator, and takes catch per unit effort (CPUE), as well as biomass survey data into account. The ad hoc tuned VPA is based on the Laurec-Shepherd tuning algorithm and utilizes catch-at-age and effort information. Applications of an age-structured model, which takes both CPUE and catch-at-age data into account, provides similar results to the production model if more weight is given to the CPUE data than the catch-at-age data and similar results to the ad hoc tuned VPA if more weight is given to the catch-at-age data rather than the CPUE data. This led Punt (1993) to conclude that the discrepancies between the various sets of results obtained from surplus production model and ad hoc tuned VPA methods are a consequence of a conflict between the catch-at-age data and the CPUE data and that they are not primarily a result of differences in the two assessment methods. However, the above two approaches are based on certain assumptions regarding recruitment, natural mortality and fishing selectivity. An attempt was made to obtain estimates of fishing selectivity-at-age from an age-structured production model. It is commonly assumed that selectivity-at-age has a slope of zero at older age classes. The estimates obtained all suggest that selectivity-at-age for older age classes (> 2 to 3 years) decreases with age. The results obtained in this study also indicate that the conflict between the observed trends in the catch-at-age data and the CPUE data can be basically resolved by assuming that for older age classes selectivity-at-age decreases.
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Daukste, Liene. "Mathematical Modelling of Cancer Cell Population Dynamics." Thesis, University of Canterbury. Department of Mathematics and Statistics, 2012. http://hdl.handle.net/10092/10057.
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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.
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Liu, Shouzong. "AGE-STRUCTURED PREDATOR-PREY MODELS." OpenSIUC, 2018. https://opensiuc.lib.siu.edu/dissertations/1577.
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In this thesis, we study the population dynamics of predator-prey interactions described by mathematical models with age/stage structures. We first consider fixed development times for predators and prey and develop a stage-structured predator-prey model with Holling type II functional response. The analysis shows that the threshold dynamics holds. That is, the predator-extinction equilibrium is globally stable if the net reproductive number of the predator $\mathcal{R}_0$ is less than $1$, while the predator population persists if $\mathcal{R}_0$ is greater than $1$. Numerical simulations are carried out to demonstrate and extend our theoretical results. A general maturation function for predators is then assumed, and an age-structured predator-prey model with no age structure for prey is formulated. Conditions for the existence and local stabilities of equilibria are obtained. The global stability of the predator-extinction equilibrium is proved by constructing a Lyapunov functional. Finally, we consider a special case of the maturation function discussed before. More specifically, we assume that the development times of predators follow a shifted Gamma distribution and then transfer the previous model into a system of differential-integral equations. We consider the existence and local stabilities of equilibria. Conditions for existence of Hopf bifurcation are given when the shape parameters of Gamma distributions are $1$ and $2$.
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Toth, Damon. "Analysis of age-structured chemostat models /." Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/6780.
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Cherif, Alhaji. "Mathematical evolutionary epidemiology : limited epitopes, evolution of strain structures and age-specificity." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:28dec0f4-e6da-466a-905c-d875f132415e.
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We investigate the biological constraints determined by the complex relationships between ecological and immunological processes of host-pathogen interactions, with emphasis on influenza viruses in human, which are responsible for a number of pandemics in the last 150 years. We begin by discussing prolegomenous reviews of historical perspectives on the use of theoretical modelling as a complementary tool in public health and epidemiology, current biological background motivating the objective of the thesis, and derivations of mathematical models of multi-locus-allele systems for infectious diseases with co-circulating serotypes. We provide detailed analysis of the multi-locus-allele model and its age-specific extension. In particular, we establish the necessary conditions for the local asymptotic stability of the steady states and the existence of oscillatory behaviours. For the age-structured model, results on the existence of a mild solution and stability conditions are presented. Numerical studies of various strain spaces show that the dynamic features are preserved. Specifically, we demonstrate that discrete antigenic forms of pathogens can exhibit three distinct dynamic features, where antigenic variants (i) fully self-organize and co-exist with no strain structure (NSS), (ii) sort themselves into discrete strain structure (DSS) with non-overlapping or minimally overlapping clusters under the principle of competitive exclusion, or (iii) exhibit cyclical strain structure (CSS) where dominant antigenic types are cyclically replaced with sharp epidemics dominated by (1) a single strain dominance with irregular emergence and re-emergence of certain pathogenic forms, (2) ordered alternating appearance of a single antigenic type in periodic or quasi-periodic form similar to periodic travelling waves, (3) erratic appearance and disappearance of synchrony between discrete antigenic types, and (4) phase-synchronization with uncorrelated amplitudes. These analyses allow us to gain insight into the age-specific immunological profile in order to untangle the effects of strain structures as captured by the clustering behaviours, and to provide public health implications. The age-structured model can be used to investigate the effect of age-specific targeting for public health purposes.
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Li, Linlin. "Analyse mathématique d'un modèle d'équations aux dérivées partielles décrivant l'adaptation des moustiques face à l'usage des insecticides." Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0097/document.
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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-solutionsThis 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
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Ejigu, Amsalework Ayele. "Mathematical modelling of HIV/AIDS transmission under treatment structured by age of infection." Thesis, Stellenbosch : University of Stellenbosch, 2011. http://hdl.handle.net/10019.1/6628.
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Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2011.Includes bibliography.
ENGLISH ABSTRACT: This thesis takes into account the different levels of infectiousness of the human immunodeficiency virus (HIV) infected individuals throughout their period of infection. Infectiousness depends on the time since infection. It is high shortly after the infection occurs and then much lower for several years, and thereafter a higher plateau is reached before the acquired immunodeficiency syndrome (AIDS) phase sets in. In line with this, we formulated a mathematical model which is structured according to the age of infection. To understand the dynamics of the disease, we first discuss and analyse a simple model in which the age of infection is not considered, but progression of the HIV-AIDS transmission is taken into consideration by introducing three stages of infection. Analysis of these models tells us that the disease can be eradicated from the population only if on average one infected individual infects less than one person in his or her infectious period, otherwise the disease persists. To investigate the reduction of the number of infections caused by a single infectious individual to less than one, we introduce different treatment strategies for a model which depends on the age of infection, and we analyse it numerically. Current strategies amount to introducing treatment only at a late stage of infection when the infected individual has already lived through most of the infectious period. From our numerical results, this strategy does not result in eradication of the disease, even though it does reduce the burden for the individual. To eradicate the disease from the population, everyone would need to be HIV tested regularly and undergo immediate treatment if found positive.
AFRIKAANSE OPSOMMING: Hierdie tesis hou rekening met die verskillende aansteeklikheidsvlakke van die menslike immuniteitsgebreksvirus (MIV) deur besmette individue gedurende hulle aansteeklikheidstydperk. Die graad van aansteeklikheid hang af van die tydperk sedert infeksie. Dit is hoog kort nadat die infeksie plaasvind en daarna heelwat laer vir etlike jare, en dan volg n hoer plato voordat uiteindelik die Verworwe-Immuniteitsgebreksindroom (VIGS) fase intree. In ooreenstemming hiermee, formuleer ons n wiskundige model van MIV-VIGSoordrag met n struktureer waarin die tydperk sedert infeksie bevat is. Om die dinamika van die siekte te verstaan, bespreek en analiseer ons eers n eenvoudige model sonder inagneming van die tydperk sedert infeksie, terwyl die progressie van MIV-VIGS-oordrag egter wel in ag geneem word deur die beskouing van drie stadiums van infeksie. Analise van die modelle wys dat die siekte in die bevolking slegs uitgeroei kan word as elke besmette mens gemiddeld minder as een ander individu aansteek gedurende die tydperk waarin hy of sy self besmet is, anders sal die siekte voortduur. Vir die ondersoek oor hoe om die aantal infeksies per besmette individu tot onder die waarde van een te verlaag, beskou ons verskeie behandelingsstrategiee binne die model, wat afhang van die tydperk sedert infeksie, en ondersoek hulle numeries. Die huidige behandelingstrategiee kom neer op behandeling slegs gedurende die laat sta- dium van infeksie, wanneer die besmette individu reeds die grootste deel van die aansteeklikheidsperiode deurleef het. Ons numeriese resultate toon dat hierdie strategie nie lei tot uitroeiing van die siekte nie, alhoewel dit wel die las van die siekte vir die individu verminder. Om die siekte binne die bevolking uit te roei, sou elkeen gereeld vir MIV getoets moes word en indien positief gevind, dadelik met behandeling moes begin.
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Muller, Nicolas. "Études mathématiques et numériques de problèmes non-linéaires et non-locaux issus de la biologie." Thesis, Paris 5, 2013. http://www.theses.fr/2013PA05S016.
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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 LyapunovWe 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
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Koch, Erich. "Effects of cannibalism, maternal age and varying fish selectivity in age structured models of deep water hake populations." Master's thesis, University of Cape Town, 2011. http://hdl.handle.net/11427/12252.
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Includes abstract.Includes bibliographical references (leaves 55-61).
An Age Structured Model (ASM) was develop in which dynamic and density-dependent cannibalism was included as a top-down control on a modeled population of M. paradoxus which used spawner biomass and maternal based recruitment. The ASM was used to evaluate the effects cannibalism had on age structure, recruitment and spawner biomass of the modeled population. The development of the model was described and evaluated with special emphasis on incorporating cannibalism and maternal based recruitment.
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Alawneh, Zakaria Mohammad. "A numerical method for solving certain nonlinear integral equations arising in age-structured populations dynamics." Diss., The University of Arizona, 1990. http://hdl.handle.net/10150/184984.
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In this thesis we study the existence and stability of positive equilibrium of a general model for the dynamics of several interacting, age-structured population. We begin with the formulation and proof of a global existence theorem for the initial value problem. The proof of this theorem is used to develop an algorithm and a FORTRAN code for the numerical solution of initial value problems for the single species case. This computer program is used to study prototype models for the dynamics of a population whose fertility and mortality rates exhibit an "Allee effect". This is done from a bifurcation theoretic point of view, using the inherent net reproductive rate as a bifurcating parameter. An unstable "left" bifurcation is found. Multi-equilibria and various kinds of oscillations are studied as a function of r, the fertility window, and the nature of the density dependence.
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Pralgauskaitė, Raminta. "Apie vieną, vaikus globojančios populiacijos modelį." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2006~D_20140702_191425-19236.
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Darbe pateiktas populiacijos dinamikos modelis, kuriame atsižvelgiama į amžių, patelių nėštumą, vaikų priežiūrą, ekologinius veiksnius. Skirtingų lyčių poros sudaromos naudojant harmoninio vidurkio funkciją, ir laikoma, kad poros egzistuoja tik dauginimosi periodu. Daugumoje populiacijų jauniklius prižiūri tik motinos, todėl laikoma, kad jaunikliai miršta, jei žūva juos prižiūrinti patelė. Kiekvienas individas turi priešreproduktyvųjį, reproduktyvųjį ir poreproduktyvųjį amžiaus intervalus. Individai, esantys priešreproduktyviajame amžiaus intervale, skirstomi į jauniklius, kuriems reikalinga motinos priežiūra, bei paauglius, kurie jau yra savarankiški individai, tik dar nepasiruošę daugintis. Reproduktyvaus amžiaus individai skirstomi į patinus, neapvaisintas pateles, apvaisintas pateles ir jauniklius prižiūrinčias pateles. Modelį sudaro integrodiferencialinės lygtys dalinėmis išvestinėmis su integralinio tipo sąlygomis. Lygčių skaičius priklauso nuo biologiškai galimo maksimalaus skaičiaus palikuonių, ir jis yra baigtinis. Limituotos populiacijos atveju surandami separabilūs sprendiniai, nelimituotos populiacijos atveju įrodoma egzistavimo ir vienaties teorema.A deterministic model for a sexual age-structured population with females pregnancy, maternal care of offspring, and an environmental pressure is presented. The model involves pairs that exist for period of mating only and uses mating function of simplified harmonic mean type. All adult males are treated as singles. Each sex has pre-reproductive, reproductive, and post-reproductive age intervals. All adult individuals (of reproductive age) are divided into males, single females, pregnant females, and females taking child care. All individuals of pre-reproductive age are divided into young and juvenile groups. All young individuals are under maternal care while juveniles can live without maternal care. The model consists of integro-differential equations. Separable solutions are studied for the limited nondispersing population. The existence and uniqueness theorem is proved in the case of unlimited population.
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Picart, Delphine. "Modélisation et estimation des paramètres liés au succès reproducteur d'un ravageur de la vigne (Lobesia botrana DEN. & SCHIFF.)." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2009. http://tel.archives-ouvertes.fr/tel-00405686.
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L'objectif de ce travail de thèse est de développer un modèle mathématique pour l'étude et la compréhension de la dynamique des populations d'un insecte ravageur, l'Eudémis de la vigne, dans son écosystème. Le modèle proposé est un système d'équations aux dérivées partielles (EDP) de type hyperbolique qui décrit les variations numériques au cours du temps de la population en fonction des stades de développement, du sexe des individus et des conditions environnementales. La ressource alimentaire, la température, l'humidité et la prédation sont les principaux facteurs environnementaux du modèle expliquant les fluctuations du nombre d'individus au cours du temps. Les différences de développement qui existent dans une cohorte d'Eudémis sont aussi modélisées pour affiner les prédictions du modèle. A partir de données expérimentales obtenues par les entomologistes de l'INRA, les paramètres du modèle sont estimés. Ce modèle ainsi ajusté nous permet alors d'étudier quelques aspects biologiques et écologiques de l'insecte comme par exemple l'impact de scénarios climatiques sur le ponte des femelles ou sur la dynamique d'attaque de la vigne par les jeunes larves. Les analyses mathématique et numérique du modèle mathématique et des problèmes d'estimation des paramètres sont développes dans cette thèse.
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Jeunesse, Paulien. "Estimation non paramétrique du taux de mort dans un modèle de population générale : Théorie et applications. A new inference strategy for general population mortality tables Nonparametric adaptive inference of birth and death models in a large population limit Nonparametric inference of age-structured models in a large population limit with interactions, immigration and characteristics Nonparametric test of time dependance of age-structured models in a large population limit." Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLED013.
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L’étude du taux de mortalité dans des modèles de population humaine ou en biologie est le cœur de ce travail. Cette thèse se situe à la frontière de la statistique des processus, de la statistique non-paramétrique et de l’analyse.Dans une première partie, centrée sur une problématique actuarielle, un algorithme est proposé pour estimer les tables de mortalité, utiles en assurance. Cet algorithme se base sur un modèle déterministe de population. Ces nouvelles estimations améliorent les résultats actuels en prenant en compte la dynamique globale de la population. Ainsi les naissances sont incorporées dans le modèle pour calculer le taux de mort. De plus, ces estimations sont mises en lien avec les travaux précédents, assurant ainsi la continuité théorique de notre travail.Dans une deuxième partie, nous nous intéressons à l’estimation du taux de mortalité dans un modèle stochastique de population. Cela nous pousse à utiliser des arguments propres à la statistique des processus et à la statistique non-paramétrique. On trouve alors des estimateurs non-paramétriques adaptatifs dans un cadre anisotrope pour la mortalité et la densité de population, ainsi que des inégalités de concentration non asymptotiques quantifiant la distance entre le modèle stochastique et le modèle déterministe limite utilisé dans la première partie. On montre que ces estimateurs restent optimaux dans un modèle où le taux de mort dépend d’interactions, comme dans le cas de la population logistique.Dans une troisième partie, on considère la réalisation d’un test pour détecter la présence d’interactions dans le taux de mortalité. Ce test permet en réalité de juger de la dépendance temporelle de ce taux. Sous une hypothèse, on montre alors qu’il est possible de détecter la présence d’interactions. Un algorithme pratique est proposé pour réaliser ce testIn this thesis, we study the mortality rate in different population models to apply our results to demography or biology. The mathematical framework includes statistics of process, nonparametric estimations and analysis.In a first part, an algorithm is proposed to estimate the mortality tables. This problematic comes from actuarial science and the aim is to apply our results in the insurance field. This algorithm is founded on a deterministic population model. The new estimates we gets improve the actual results. Its advantage is to take into account the global population dynamics. Thanks to that, births are used in our model to compute the mortality rate. Finally these estimations are linked with the precedent works. This is a point of great importance in the field of actuarial science.In a second part, we are interested in the estimation of the mortality rate in a stochastic population model. We need to use the tools coming from nonparametric estimations and statistics of process to do so. Indeed, the mortality rate is a function of two parameters, the time and the age. We propose minimax optimal and adaptive estimators for the mortality and the population density. We also demonstrate some non asymptotics concentration inequalities. These inequalities quantifiy the deviation between the stochastic process and its deterministic limit we used in the first part. We prove that our estimators are still optimal in a model where the mortality is influenced by interactions. This is for example the case for the logistic population.In a third part, we consider the testing problem to detect the existence of interactions. This test is in fact designed to detect the time dependance of the mortality rate. Under the assumption the time dependance in the mortality rate comes only from the interactions, we can detect the presence of interactions. Finally we propose an algorithm to do this test
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Seydi, Ousmane. "Perturbations singulières des systèmes dynamiques en dimension infinie : théorie et applications." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-00991857.
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L'objectif de cette thèse est d'étudier et de donner des outils pour la compréhension des problèmes de perturbations singulières pour des modèles épidémiques et des problèmes de dynamiques de populations. Les modèles considérés sont des équations structurées en âge qui peuvent dans certains cas se réécrire comme des équations à retard. L'étude de ces classes d'exemples s'est faite avec succès et a permis de comprendre et de mettre en évidence toute la complexité et l'étendue de ces problèmes. Comme on peut le remarquer dans la littérature, l'une des clés fondamentales à la compréhension de ces problèmes est l'étude des variétés normalement hyperboliques en dimension infinie que nous avons largement étudiées dans cette thèse. L'approche utilisée est la méthode de Lyapunov-Perron. Ce qui nous a amené à étudier les problèmes de persistance et d'existence de trichotomie (dichotomie) exponentielle qui sont des éléments fondamentaux dans l'utilisation de cette méthode.
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Richard, Quentin. "Comportement asymptotique de modèles de populations structurées." Thesis, Bourgogne Franche-Comté, 2018. http://www.theses.fr/2018UBFCD050/document.
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Dans cette thèse nous regardons plusieurs modèles de populations structurés s’écrivant à l’aide d’équations de transport. Le caractère bien posé ainsi que la positivité des solutions sont montrés de manière systématique au sens des sémiologues dans un cadre L1. Un premier travail est consacré à un système de type proie prédateur structuré en âge. Une étude de stabilité des équilibres nous permet de formuler explicitement un seuil un seuil d’extinction ainsi qu’in seuil pouvant amener à l’explosion des populations. On obtient numériquement la possibilité d’un cycle limite ainsi que la convergence vers un équilibre de coexistence des populations. Dans un cas particulier, ce modèle se réécrit comme un système différentiel à retard. A l’aide de fonctionnelle de Lyapunov, on montre la stabilité globale de cet équilibre sous certaines conditions. On étudie également 2 modèles structuré en taille, issus de la dynamique cellulaire. L’un est composé de deux équations de transport où la cellule peut être soit prolifèrent soit quiescente ; et le deuxième est une équation de type transport/ diffusion avec des conditions aux bords FELLER. On vérifie à chaque fois l’irréductibilité du semi groupe puis des arguments de faibles capacité L1 nous donne l’existence d’un « gap spectral » sous certaines conditions. On démontre ainsi dans certains cas la croissance exponentielle asynchrone du semi groupeThis thesis is dedicated to some structured populations models described with transport or transport-diffusion equations. The well-posedness, in the semigroupes setting in L1 and the positivity of the solutions are systematically shown. A first work is dedicated to an age-structured predator/prey system. A stability study of the equilibria allow us to give explicit formulations of an extinction threshold and an threshold which can lead to explosion of solutions. We numerically obtain the possibility to get a limit cycle and the convergence to a coexistence equilibrium of the populations. In a specific case, this model rewrites as a delay differential system. Using Lyapunov functional, we show the global stability of this equilibrium under some assumptions. We also study two size-structured models that come from cellular dynamics. The first one consists on two transport equations, where the cell can either proliferate or be quiescent, and the second one is a transport-diffusion equation with Feller boundary conditions. The irreducibility of the semigroup governing this latter model is always satisfied using the Hopf maximum principle. However, the irreducibility for the first model is true only under a necessary and sufficient condition that we give. We also show for these two models, using some weak compactness arguments in L1, the existence of a `spectral gap' (essential type strictly less than the type) ensuring the asynchronous exponential growth of the semigroup
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Mohamed, Mostafa Kamel Saber. "Harvesting of Age Structured Fish Populations." Doctoral thesis, 2005. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2005021812.
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The aim of this thesis is to define and study harvesting models of fish populations. These models are applied to particular fish species e.g., haddock and cod. The thesis is divided into five chapters: The first chapter is considered as an introductory one. In it, basics of fish biology and the recruitment process are defined. Two simple recruitment models known by the names Ricker and Beverton-Holt are used. In the second chapter the generalized Leslie model or Usher model is introduced. In section 2.2, some matrix theory is presented. For this matrix model, the net reproductive number is defined and studied in section 2.3. It turns out to be more useful than the spectral radius. In section 2.4, this study is extended to nonlinear matrix models. The nonlinearity, however, is defined only by the recruitment process. This allows to determine the equilibrium components. Finally section 2.5, the local stability of nonlinear matrix models is analyzed. Harvesting of such general matrix model is defined in chapter 3. We distinguish three different harvesting models (selective, net and semicontinuous harvesting models). In chapter 4, these harvesting models are then applied to concrete fish populations and analyzed with respect to its various parameters. In chapter 5, the stability is studied again along the lines of the paper of Levin, Goodyear [18]. The key results in this study are: 1) The maximum sustainable yields for selective harvesting and net harvesting are rather close. 2) Semicontinuous harvesting is more realistic harvesting models. 3) From a quantitative point of view, the choice of the recruitment function is important. 4) Harvesting process increases mortality and stability when we used Ricker recruitment model. 5) Stability of populations always holds if we use Beverton-Holt recruitment model.
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Farinaz, Forouzannia. "Dynamics of Multi-strain Age-structured Model for Malaria Transmission." 2013. http://hdl.handle.net/1993/22060.
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The thesis is based on the use of mathematical modeling and analysis to gain insightinto the transmission dynamics of malaria in a community. A new deterministic
model for assessing the role of age-structure on the disease dynamics is designed.
The model undergoes backward bifurcation, a dynamic phenomenon characterized
by the co-existence of a stable disease-free and an endemic equilibrium of the model
when the associated reproduction number is less than unity. It is shown that adding
age-structure to the basic model for malaria transmission does not alter its essential
qualitative dynamics. The study is extended to incorporate the use of anti-malaria
drugs. Numerical simulations of the extended model suggest that for the case when
treatment does not cause drug resistance (and the reproduction number of each of the
two strains exceed unity), the model undergoes competitive exclusion. The impact
of various effectiveness levels of the treatment strategy is assessed.
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Forouzannia, Farinaz. "Dynamics of Multi-strain Age-structured Model for Malaria Transmission." 2013. http://hdl.handle.net/1993/22060.
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The thesis is based on the use of mathematical modeling and analysis to gain insightinto the transmission dynamics of malaria in a community. A new deterministic
model for assessing the role of age-structure on the disease dynamics is designed.
The model undergoes backward bifurcation, a dynamic phenomenon characterized
by the co-existence of a stable disease-free and an endemic equilibrium of the model
when the associated reproduction number is less than unity. It is shown that adding
age-structure to the basic model for malaria transmission does not alter its essential
qualitative dynamics. The study is extended to incorporate the use of anti-malaria
drugs. Numerical simulations of the extended model suggest that for the case when
treatment does not cause drug resistance (and the reproduction number of each of the
two strains exceed unity), the model undergoes competitive exclusion. The impact
of various effectiveness levels of the treatment strategy is assessed.
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賴怡汝. "Stock Assessment of Indian Bigeye Tuna (Tunnus obesus)by Age Structured Production Model." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/88274654433996405260.
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Wu, Wei-Jang, and 吳維章. "Stock assessment of swordfish in the South Atlantic Ocean using the age-structured production model." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/96312944029919300867.
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碩士國立臺灣大學
海洋研究所
98
Traditionally ICCAT uses the surplus production model (e.g., Schaefer 1957) to calculate the biological reference points when performing stock assessment on the southern Atlantic swordfish stock, but the growth and mortality between the age classes cannot be explained by this single production function. In this study, a age-structured production model (ASPM) which can include the information of selectivity, weight-at-age, maturity-at-age and natural mortality information was used for the stock assessment of swordfish in the South Atlantic Ocean. The ASPM model was fitted to the catch-rate data for the Japanese, Taiwan, Spain, Brazil and Uruguay longline fisheries, as these fleets take the bulk of the catch of swordfish in the Sorth Atlantic Ocean. The results of this study showed that the Southern Atlantic swordfish stock’s was slightly overfished by F2008/FMSY equal to 0.89 and SSB2008/SSBMSY was slightly smaller than 1（0.91）. A total allowable catch of 11,000 tons or <11,000 tons was suggested to recover stock status for the projected fifteen years. Monte Carlo simulation was used to evaluate the impact of errors in input parameters on the quantities of management interest. The sensitivity analysis showed that errors in natural mortality, CPUE, and catch have the substantial effect on the stock status evaluations. Future research on these fields is highlight and should be enhanced to reduce the uncertainty of the stock assessment.
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Chen, Ying-Ru, and 陳盈如. "Stock assessment of swordfish (Xiphias gladius) in the Indian Ocean using the age-structured model." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/78184615278067417804.
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碩士國立臺灣海洋大學
環境生物與漁業科學學系
96
Abstract Swordfish (Xiphias gladius, Linnaeus 1758) in the Indian Ocean were mainly caught by Taiwanese and Japanese longline fisheries in the early years. Since 1990’s the catch increased substantially due to seasonal targeting of Taiwanese longline fishery and exploitation of Australia, France-Reunion, Spanish and Sri Lankan. Most previous assessments of swordfish in the Indian Ocean have been based on trends in CPUE and the results of production model assessments. Swordfish are known to be sexually dimorphic and previous assessments ignored the age- and sex- structured dynamics of population. Due to absence of sex-specific information, however, an age-structured assessment model without sex factor was conducted for evaluating the population status of the swordfish in the Indian Ocean. Based on the results of the base-case analysis, the fleet-aggregated fishing intensity in 2005 was higher than that at which MSY is achieved and the spawning stock biomass in 2005 was about 37% of its unfished level and about 1.88 times of that at which MSY is achieved. The result of the sensitivity analyses indicated that the results of assessment model are sensitive to the values of natural mortality. Nevertheless, the least optimistic results, which indicated that the spawning stock biomass in 2005 was remaining about 27% of its unfished level but still higher that at which MSY is achieved, only occurred when natural mortality was assumed to be a relatively low value. Therefore, the results of this study indicate that there is probable overfishing of the swordfish stock in the Indian Ocean in recent years while the stock currently appears not to be in an overfished state.
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Wang, Sheng-Ping. "Sex-specific age-structured model for stock assessment of swordfish (Xiphias gladius) in the North Pacific Ocean." 2004. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0001-2707200420200600.
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Ma, Chih-Tsung, and 馬志宗. "Stock assessment and risk analysis for Indian Ocean albacore(Thunnus alalunga) using an age-structured production model." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/76602607890505650493.
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Lin, Yu-Yong, and 林鈺詠. "Stock assessment of dolphinfish (Coryphaena hippurus) in the eastern waters off Taiwan using age-structured production model." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/k7wztx.
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碩士國立臺灣海洋大學
環境生物與漁業科學學系
107
The dolphinfish (Coryphaena hippurus) is one of the most important economic species for Taiwanese offshore and coastal fishery and most catches were caught in the eastern waters of Taiwan. Therefore, dolphinfish is an important target species for fishery in the eastern waters of Taiwan. The data used in the study were historical total catches, length-frequency and daily auction data of dolphinfish from Yilan, Haulien, and Taitung. In this study, the population status of dolphinfish in the eastern off Taiwan was evaluated using age-structured production model (ASPM). The relative abundance index was based on the catch per unit effort (CPUE) standardized using general linear model (GLM) based on daily auction data. The base-case results of ASPM indicated that the catches were mainly consisted of fishes with 1-year-old. The spawning stock biomass decreased gradually with increase of catch, but the current fishing mortality was still below the maximum sustainable yield (MSY) level and the spawning stock biomass was slightly higher than the MSY level. The result of the sensitivity analysis indicated that the results of assessment model are sensitive to the values of natural mortality and steepness. The current fishing mortality was below the MSY level in most of cases, but the spawning stock biomass was close to or slightly higher than the MSY level. Based on the results of this study, there is a higher probability that the dolphinfish in the eastern waters of Taiwan was moderately exploited currently, but there is also a risk that the spawning stock biomass may not maintain at the MSY levels. Therefore, in order to maintain the sustainability of this stock, it is necessary to continuously evaluate and monitor the stock dynamics of the resource and exploitation for the fishery.
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Wang, Sheng-Ping, and 王勝平. "Sex-specific age-structured model for stock assessment of swordfish (Xiphias gladius) in the North Pacific Ocean." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/74539175942181135822.
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博士國立臺灣大學
海洋研究所
92
Swordfish are sexually dimorphic. However, previous assessments of the status of swordfish in the North Pacific Ocean have ignored this. A sex-specific age-structured assessment model was therefore constructed for the stock of swordfish in the North Pacific Ocean. This model was fitted to the catch, catch-rate and length-frequency data for the Japanese high-seas and Hawaii-based longline fisheries, as these fleets take the bulk of the catch of swordfish in the North Pacific Ocean. The results of this assessment indicate that the spawning stock biomass in 2000 remains at a high (~70%) percentage of its unfished level and that the fleet-aggregated fishing intensity in 2000 was only about 12% of that at which MSY is achieved. These results pertain to a base-case analysis. Although the results of the assessment model are sensitive to the values for natural mortality and the steepness of the stock-recruitment relationship, even the most pessimistic results of the sensitivity analyses conducted indicate that the spawning stock biomass in 2000 was larger than half of its unfished level and that the fleet-aggregated fishing intensity in 2000 was less than 25% of that at which MSY is achieved. Therefore, the swordfish stock in the North Pacific Ocean appears to be relatively stable at the current level of exploitation. Forward projections based on samples from a Bayesian posterior distribution indicate that there is negligible risk of the stock dropping below 40% of the unfished spawning stock biomass if fleet-aggregated fishing intensity remains at the current level. The performance of the method of stock assessment applied in this study has not been evaluated using Monte Carlo simulation. Therefore, Monte Carlo simulation is used to evaluate the impact of observation errors, and errors when setting the values for some of the parameters of the model that cannot be estimated from the data available for assessment purposes. The observation error associated with the catch-rate indices has a larger impact on estimation ability than errors when measuring catches and when sampling catches for length-frequency. Improved performance, in terms of both the accuracy and precision of the estimates of quantities of management interest, can be obtained by increasing the length-frequency sample sizes. The estimates of spawning stock biomass, MSY, and (to a lesser extent) fishing intensity are substantially more biased when the assessment ignores sexual dimorphism. The ratios of current to unfished spawning stock biomass and to the spawning biomass corresponding to MSY were found to be the quantities estimated most robustly of those considered.
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(9750296), Joan L. Ponce. "Structured Epidemiological Models with Applications to COVID-19, Ebola, and Childhood-Diseases." Thesis, 2020.
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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.
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.
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.
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Su, Nan-Jay, and 蘇楠傑. "A spatially, sex- and age-structured model for stock assessment of blue marlin (Makaira nigricans) in the Pacific Ocean." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/15936861151570925098.
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博士國立臺灣大學
海洋研究所
99
Blue marlin are widely distributed throughout tropical and temperate waters in the Pacific Ocean. However, the preference of this species for particular habitats may impact its vulnerability to being caught. The relationship between spatio-temporal patterns of blue marlin abundance and environmental factors is examined using generalized additive models (GAMs) fitted to catch and effort data from longline fisheries. Spatial distributions of relative density of blue marlin indicate that there is seasonal variation in the distribution of blue marlin, which appears to be related to shifts in sea surface temperature (SST). However, previous stock assessments for blue marlin in the Pacific Ocean have ignored the possible impacts of seasonal movement and sexual dimorphism in growth. A spatially sex-specific age-structured population dynamics model was therefore constructed and fitted to the catch-rate and length- frequency data for the Japanese and Taiwanese pelagic tuna longline fisheries, along with information on the relative density of the population over space derived from the GAM. Assessments that account for seasonal movement and sexual dimorphism indicate that the blue marlin population in the Pacific Ocean is in a healthy condition, with the current spawning stock biomass (S2006) at a fairly high fraction of its unfished level (S2006/S0 = 0.81) and larger than that corresponding to maximum sustainable yield (MSY) (S2006/SMSY = 1.66) and the current fishing mortality (F2006) less than that needed to achieve MSY (F2006/FMSY = 0.51). A risk analysis suggests that the status of this population will remain optimistic if exploitation rates are maintained at the current level. The estimation performance of the assessment model is examined using Monte Carlo simulation. This shows that the outcomes of the assessment are sensitive to the values assumed for natural mortality and stock-recruitment steepness. The uncertainty related to these two parameters could be reduced through fishery-independent abundance surveys and tagging studies. Although estimates of biomass, MSY, and fishing intensity are substantially biased when the assessment method ignores seasonal movement and sexual dimorphism, the relative biomass measure S2006/S0 appears to be the most robust among the quantities considered. Therefore, assessment methods for blue marlin in the Pacific Ocean need to take seasonal migration and sex-structure into account to reduce the uncertainty of parameter estimates, and thus improve the accuracy of stock assessments.
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Vaz, João. "Harvest control rule vs optimal harvesting of an age-structured population: the case of the Ibero-Atlantic Sardine Fishery." Master's thesis, 2015. http://hdl.handle.net/10362/17487.
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Research MastersIn this study we apply an age-structured bio-economic model to the Ibero-Atlantic sardine stock, and compute an optimal harvesting strategy. We compare it with the ongoing harvest control rule, which overlooks economic incentives. We show that the optimal plan entails greater net returns from the fishery, though at a cost of reducing biomass below acceptable reference points. By incorporating precautionary constraints, we find that an optimal plan still yields higher economic returns, while better adhering to stock-recovery objectives.
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Wang, Guanyu. "Age structured model for simulation T cell differentiation during normal development and in leukemogenesis = Model zur altersabhängigen Simulation der T-Zell-Differenzierung während der normalen Entwicklung und während der Leukämogenese /." 2005. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=014178432&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
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"Spatial spread of rabies in wildlife." Doctoral diss., 2013. http://hdl.handle.net/2286/R.I.20921.
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abstract: Rabies disease remains enzootic among raccoons, skunks, foxes and bats in the United States. It is of primary concern for public-health agencies to control spatial spread of rabies in wildlife and its potential spillover infection of domestic animals and humans. Rabies is invariably fatal in wildlife if untreated, with a non-negligible incubation period. Understanding how this latency affects spatial spread of rabies in wildlife is the concern of chapter 2 and 3. Chapter 1 deals with the background of mathematical models for rabies and lists main objectives. In chapter 2, a reaction-diffusion susceptible-exposed-infected (SEI) model and a delayed diffusive susceptible-infected (SI) model are constructed to describe the same epidemic process -- rabies spread in foxes. For the delayed diffusive model a non-local infection term with delay is resulted from modeling the dispersal during incubation stage. Comparison is made regarding minimum traveling wave speeds of the two models, which are verified using numerical experiments. In chapter 3, starting with two Kermack and McKendrick's models where infectivity, death rate and diffusion rate of infected individuals can depend on the age of infection, the asymptotic speed of spread $c^\ast$ for the cumulated force of infection can be analyzed. For the special case of fixed incubation period, the asymptotic speed of spread is governed by the same integral equation for both models. Although explicit solutions for $c^\ast$ are difficult to obtain, assuming that diffusion coefficient of incubating animals is small, $c^\ast$ can be estimated in terms of model parameter values. Chapter 4 considers the implementation of realistic landscape in simulation of rabies spread in skunks and bats in northeast Texas. The Finite Element Method (FEM) is adopted because the irregular shapes of realistic landscape naturally lead to unstructured grids in the spatial domain. This implementation leads to a more accurate description of skunk rabies cases distributions.Dissertation/Thesis
Ph.D. Mathematics 2013
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Paquin-Lefebvre, Frédéric. "Sur un modèle d'érythropoïèse comportant un taux de mortalité dynamique." Thèse, 2015. http://hdl.handle.net/1866/11690.
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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.
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Soares, Cíntia Dalila. "Évolution dans des populations structurées en classes." Thèse, 2019. http://hdl.handle.net/1866/22666.
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