Die invasive Meningokokkenerkrankung stellt weltweit mit einer Letalität von 5-10% trotz antibiotischer Therapie eine Herausforderung dar. Ein spezifisches Virulenzgen, welches die Schwere der Meningokokkenerkrankung bestimmt, konnte bisher nicht definiert werden. Vorangegangene Studien zeigen eine Korrelation der Letalität mit der Bakterienlast, Unterschiede bezüglich der Letalität je nach Serogruppe, eine erhöhte Letalität bei Infektionen mit sogenannten hyperletalen Feintypen (bisher nicht veröffentlichte Daten des NRZMHi) sowie einen Unterschied in der maximal in Flüssigkultur erreichten Konzentration der Bakterien zwischen invasiven Stämmen und Trägerstämmen. In dieser Arbeit wurden mögliche Gründe für die Hyperletalität bestimmter Meningokokkentypen experimentell untersucht. Insbesondere wird die Frage analysiert, ob die hyperletalen Meningokokkentypen mit einer höheren bakteriellen Last im Blut assoziiert sind und ob sie andere Wachstumscharakteristiken im Vergleich zu ihren Kontrollstämmen in vitro zeigen. Hierzu erfolgte mittels quantitativer Echtzeit-Polymerase-Kettenreaktion die Bestimmung der bakteriellen Last in 62 Blutproben von Patienten mit bestätigter invasiver Meningokokkenerkrankung über den Nachweis des ctrA-Gens. Darunter waren elf Proben des hyperletalen Feintyps B:P1.7-2,4:F1-5 und fünf Proben des hyperletalen Feintyps C:P1.5,2:F3-3. Die Wachstumsversuche wurden mit 30 zufällig gewählten Stämmen der hyperletalen Feintypen B:P1.7-2,4:F1-5, C:P1.5-1,10-8:F3-6 und C:P1.5,2:F3-3 mit ihren jeweiligen nach Alter und Geschlecht abgeglichenen nicht zu der Gruppe der hyperletalen Feintypen gehörenden Kontrollstämmen in dem Medium PPM+ durchgeführt. Die Wachstumsgeschwindigkeit μ sowie die Kapazität A (maximale Konzentrationszunahme als Logarithmus der gemessenen OD im Verhältnis zur Ausgangsdichte ODT0) wurden durch nicht-lineare Regression anhand der modifizierten Gompertz-Funktion ermittelt. Die Messung der optischen Dichte erfolgte alle 30 Minuten über 16 Stunden bei 620nm durch das Gerät TECAN Infinite 200 Pro (Tecan Group Ltd., Männedorf / Schweiz). Die Methode wurde anhand einer publizierten Studie zwischen Trägerstämmen und invasiven Stämmen (Schoen et al., 2014) validiert und bestätigte einen marginalen Unterschied in der optischen Dichte (p=0,057, Wilcoxon-Test) zwischen den Gruppen. Es zeigte sich kein Unterschied in der Wachstumsgeschwindigkeit. Aus den Ergebnissen dieser Arbeit können drei wesentliche Schlussfolgerungen gezogen werden: 1.) Die Bakterienlast in dieser Stichprobe ist, entgegen der Literatur, nicht abhängig von der Serogruppe und dem Feintyp, jedoch von der Krankheitsmanifestation. 2.) Die Kapazität A ist in der Gruppe der „hyperletalen“ Typen im Vergleich zu den Kontrollstämmen möglicherweise höher. 3.) Größere Stichproben (Nativmaterial, Stämme) sind erforderlich, um die Beobachtungen dieser Studie zu bestätigen. / The invasive meningococcal disease still has a case fatality rate of 5 to 10 percent despite antibiotic treatment. A specific virulence gene, which determines disease severity could not be determined so far. Earlier studies have shown a correlation between lethality and bacterial load, differences in lethality between serogroups, a disproportionately high lethality of infections with distinct meningococcal finetypes (data not yet published by the NRZMHi) as well as a difference in the maximum concentration of bacteria in fluid culture between invasive and carrier strains. This dissertation analyses possible causes for the higher fatality rate of certain meningococcal finetypes. It tries to answer the question whether the so called highly lethal meningococcal finetypes are associated with a higher bacterial load in blood and whether they show different growth characteristics in comparison to their control strains in vitro. Bacterial loads in 62 blood samples from patients with confirmed invasive meningococcal disease were measured by real-time polymerase chain reaction targeting the ctrA gene. The samples contained eleven samples of the highly lethal meningococcal finetype B:P1.7-2,4:F1-5 and five samples of the highly lethal meningococcal finetype C:P1.5,2:F3-3. Growth characteristics of 30 randomly selected strains pertaining to the highly lethal finetypes B:P1.7-2,4:F1-5, C:P1.5-1,10-8:F3-6 and C:P1.5,2:F3-3 were compared to strains from age- and sex- matched controls in proteose-peptone-medium (PPM+). Growth rates (μ) and maximum densities (A) were estimated by non-linear regression on the basis of the modified Gompertz function. Optical density at 620nm was measured every 30 minutes over 16 hours using a heatable plate reader (Tecan, Maennedorf, Switzerland). The method was validated on a published sample of invasive and carrier strains (Schoen et al., 2014) confirming marginally significant differences in maximal densities (p=0,057, Wilcoxon test), yet not growth rates, between groups. In summary we conclude: 1. The bacterial load in this sampling is not dependent on serogroup and finetype, but on the clinical picture. This finding contrasts the current literature. 2. The maximum density A is possibly higher in the group of highly lethal finetypes in comparison to the control strains. 3. Larger samples of both patient material and bacterial strains are required to confirm the observations of this study.

Submitted by Bruna Rodrigues (bruna92rodrigues@yahoo.com.br) on 2016-10-03T11:30:55Z No. of bitstreams: 1 TeseRFR.pdf: 5229141 bytes, checksum: 6f0e842f89ed4a41892f27532248ba4a (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-10T17:37:43Z (GMT) No. of bitstreams: 1 TeseRFR.pdf: 5229141 bytes, checksum: 6f0e842f89ed4a41892f27532248ba4a (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-10T17:37:50Z (GMT) No. of bitstreams: 1 TeseRFR.pdf: 5229141 bytes, checksum: 6f0e842f89ed4a41892f27532248ba4a (MD5) / Made available in DSpace on 2016-10-10T17:37:59Z (GMT). No. of bitstreams: 1 TeseRFR.pdf: 5229141 bytes, checksum: 6f0e842f89ed4a41892f27532248ba4a (MD5) Previous issue date: 2016-04-01 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Modeling of a cure fraction, also known as long-term survivors, is a part of survival analysis. It studies cases where supposedly there are observations not susceptible to the event of interest. Such cases require special theoretical treatment, in a way that the modeling assumes the existence of such observations. We need to use some strategy to make the survival function converge to a value p 2 (0; 1), representing the cure rate. A way to model cure rates is to use defective distributions. These distributions are characterized by having probability density functions which integrate to values less than one when the domain of some of their parameters is di erent from that usually de ned. There is not so much literature about these distributions. There are at least two distributions in the literature that can be used for defective modeling: the Gompertz and inverse Gaussian distribution. The defective models have the advantage of not need the assumption of the presence of immune individuals in the data set. In order to use the defective distributions theory in a competitive way, we need a larger variety of these distributions. Therefore, the main objective of this work is to increase the number of defective distributions that can be used in the cure rate modeling. We investigate how to extend baseline models using some family of distributions. In addition, we derive a property of the Marshall-Olkin family of distributions that allows one to generate new defective models. / A modelagem da fração de cura e uma parte importante da an álise de sobrevivência. Essa área estuda os casos em que, supostamente, existem observa ções não suscetíveis ao evento de interesse. Tais casos requerem um tratamento teórico especial, de forma que a modelagem pressuponha a existência de tais observações. E necessário usar alguma estratégia para tornar a função de sobrevivência convergente para um valor p 2 (0; 1), que represente a taxa de cura. Uma forma de modelar tais frações e por meio de distribui ções defeituosas. Essas distribuições são caracterizadas por possuirem funções de densidade de probabilidade que integram em valores inferiores a um quando o domínio de alguns dos seus parâmetros e diferente daquele em que e usualmente definido. Existem, pelo menos, duas distribuições defeituosas na literatura: a Gompertz e a inversa Gaussiana. Os modelos defeituosos têm a vantagem de não precisar pressupor a presença de indivíduos imunes no conjunto de dados. Para utilizar a teoria de d istribuições defeituosas de forma competitiva e necessário uma maior variedade dessas distribuições. Portanto, o principal objetivo deste trabalho e aumentar o n úmero de distribuições defeituosas que podem ser utilizadas na modelagem de frações de curas. Nós investigamos como estender os modelos defeituosos básicos utilizando certas famílias de distribuições. Além disso, derivamos uma propriedade da famí lia Marshall-Olkin de distribuições que permite gerar uma nova classe de modelos defeituosos.

The aim of this thesis is to develop discrete fractional models of tumor growth for a given data and to estimate parameters of these models in order to have better data tting. We use discrete nabla fractional calculus because we believe the discrete counterpart of this mathematical theory will give us a better and more accurate outcome. This thesis consists of ve chapters. In the rst chapter, we give the history of the fractional calculus, and we present some basic de nitions and properties that are used in this theory. We de ne nabla fractional exponential and then nabla fractional trigonometric functions. In the second chapter, we concentrate on completely monotonic functions on R, and we introduce completely monotonic functions on discrete domain. The third chapter presents discrete Laplace N-transform table which is a great tool to nd solutions of -th order nabla fractional di erence equations. Furthermore, we nd the solution of nonhomogeneous up to rst order nabla fractional di erence equation using N-transform. In the fourth chapter, rst we give the de nition of Casoration for the set of solutions up to n-th order nabla fractional equation. Then, we state and prove some basic theorems about linear independence of the set of solutions. We focus on the solutions of up to second order nabla fractional di erence equation. We examine these solutions case by case namely, for the real and distinct characteristic roots, real and same, and complex ones. The fth chapter emphasizes the aim of this thesis. First, we give a vi brief introduction to parameter estimation with Gomperts and Logistic curves. In addition, we recall a statistical method called cross-validation for prediction. We state continuous, discrete, continuous fractional and discrete fractional forms of Gompertz and Logistic curves. We use the tumor growth data for twenty-eight mice for the comparison. These control mice were inoculated with tumors but did not receive any succeeding treatment. We claim that the discrete fractional type of sigmoidal curves have the best data tting results when they are compared to the other types of models.

Natural life history of cephalopods have been puzzling marine biologists for a long time. Fishery scientists also met with great difficulty in managing resources of squids as well as cuttlefishes. The lack of the accurate equation defining growth through time is one of the major reasons. This was due mainly to no stable characteristic for age determinations. It was known that in anatomy, stripe layers of cuttlebone are similar in embryonic development as shells of the bivalve, which has been used for age determinations. This study suggested that by taking the stripe marks on the bottom surface of the cuttlebone as quasi-daily-aging characters, it is possible to define the trend of growth of cuttlefish by (either a von Bertalanffy or Gompertz) growth equation. A semi-automatic computer processing system was designed and organized to measure the stripe area lengths (SAL) and lengths of stripe margin (LSM) for all stripe marks upon individual cuttlebone (analogous to scale reading in fishery research for the same purpose) of ¡]Sepia pharaonic Ehrenberg¡A1831¡^. A total of 21 cuttlebones were measured and the data analyzed. It appeared that the growth of the cuttlefishes are still on the stage of acceleration, and is not suitable to be represented by the VBGF curve traditionally used. Using SAL= and LSM= ' as length indicators respectively, two Gompertz growth equations were respectively estimated as followed. = 30.00*exp[-3.73*exp(-0.012*t)] ' = 23.18*exp[-4.27*exp(-0.015*t)] Two functional linear regression formulas were also prepared as: = -1.2684 + 0.7729 * L ' = -0.7829 + 0.6297 * L The above formulas can be used for the transformation between SAL (or LAM) and body length. The well-known Rosa Lee¡¦s phenomenon was not found either based on the character of SAL or LSM, implying that during the trend of growing, the mortality of Sepia pharaonic were not significantly different among different sizes of organisms. It was expected that with this breakthrough in technique and theory, additional knowledge on the populations biology of cuttlefish can be known in more detail.

Submitted by GIULIA LEMBO CATERINA null (giucaterina@hotmail.com) on 2017-04-03T21:59:24Z No. of bitstreams: 1 Giulia_Caterina_tese.pdf: 2061741 bytes, checksum: ba5089a3900a08b417c76904274f934d (MD5) / Approved for entry into archive by Luiz Galeffi (luizgaleffi@gmail.com) on 2017-04-11T20:50:43Z (GMT) No. of bitstreams: 1 caterina_gl_dr_bot.pdf: 2061741 bytes, checksum: ba5089a3900a08b417c76904274f934d (MD5) / Made available in DSpace on 2017-04-11T20:50:43Z (GMT). No. of bitstreams: 1 caterina_gl_dr_bot.pdf: 2061741 bytes, checksum: ba5089a3900a08b417c76904274f934d (MD5) Previous issue date: 2017-02-02 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Modelos de crescimento podem servir como ferramenta de planejamento de plantios florestais para o serviço público, produtores e investidores. O presente trabalho utilizou o modelo de crescimento Gompertz para analisar e comparar curvas médias de crescimento em volume de madeira com casca e sem casca por árvore de dois clones distintos de Eucalyptus grandis x Eucalyptus urophylla em diferentes densidades de plantio: 1,5m x 1,5m, 3,0m x 0,75m, 3,0m x 1,0m, e 3,0m x 1,9m. Os dados foram coletados a partir de parcelas permanentes localizadas em plantios da empresa Duratex Florestal LTDA no município de Estrela do Sul - MG em quatro idades: 24, 36, 48 e 60 meses. As análises seguiram duas abordagens. A primeira abordagem foi pela curva de crescimento utilizando o modelo Gompertz, do qual foram ajustadas as curvas médias de crescimento. Os parâmetros estimados de interesse foram a velocidade máxima de crescimento no ponto de inflexão e a abscissa da inflexão. A segunda abordagem foi pela modelagem do máximo volume com e sem casca amostrais através de modelos lineares generalizados. O efeito de clone e espaçamento foi avaliado e as médias dos maiores volumes amostrais foram, também, comparadas entre tratamentos. Os dados observados de volume com e sem casca por árvore permitiram bons ajustes do modelo de Gompertz, com o objetivo de descrever o crescimento destas variáveis ao longo do tempo. Foi possível identificar as fases juvenil, que vai até o ponto de inflexão da curva e de maturidade, que vai do ponto de inflexão até o ponto de máxima tangência nas curvas projetadas para quase todos os tratamentos. Porém, o período de dados coletados não foi o suficiente para se modelar a curva de crescimento por árvore até a senescência da curva, mesmo para os espaçamentos mais adensados. As maiores médias de velocidade máxima de crescimento individual foram encontradas no espaçamento mais amplo, 3,0m x 1,9m, para ambos os clones, assim como as maiores médias dos volumes individuais máximos com e sem casca. O clone c1 apresentou maiores médias dos volumes individuais máximos com e sem casca por árvore observados que o clone c2. A idade do plantio se mostrou essencial na discussão sobre a produtividade de diferentes arranjos de plantio. Portanto, este estudo confirma a importância do uso de curvas de crescimentos em estudos na área florestal. / Growth models can serve as a tool for forest management plans for public service, producers and investors. The present work used the Gompertz growth model to analyze and compare individual volume growth curves of three distinct clones of Eucalyptus grandis x Eucalyptus urophylla at different planting densities. Four different spacings densities were evaluated, 3.0m x 0.75m, 1.5m x 1.5m, 3.0m x 1.9m and 3.0m x 1.0m, for each clone at two different sites, São Paulo and Minas Gerais General. The data were collected from permanent plots at four ages: 24, 36, 48 and 60 months. The analyzes followed two approaches. The first approach was to adjust the growth curve using the Gompertz model to the volume data. The estimated parameters of interest, analyzed later, were the maximum velocity of growth at the inflection point and the abscissa of the inflection point. For each estimated parameter, generalized linear models were adjusted to detect the effect of location, clone and spacing. Thus, the adjustment was made for each portion of the treatments and the means of the estimated parameters were compared. The second approach was the modeling of the largest volume observed through generalized linear models. The effect of site, clone and spacing were evaluated and the means of the largest sample volumes were compared between treatments. The observed data of volume with and without bark per tree allowed good adjustments of the Gompertz model, in order to describe the growth of these variables over time. It was possible to identify the juvenile phase, which goes from first years to the point of inflection, and the maturity phase, which goes from the point of inflection to the point of maximum tangency, for almost all treatments. However, the period of data collection was not sufficient to get the curves to the senescence phase, even for the denser spaces. The spacing density 3.0m x 1.9m resulted on the higher averages of maximum individual growth velocity and on the higher mean values of the observed volumes with and without bark. Clone c1 presented higher mean values of the observed volumes with and without bark per tree than clone c2. The stand age was shown to be essential in the discussion of a productivity of different densities arrangements. Therefore, this study confirms the importance of the use of growth curves in studies in forestry.

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / Objetivou-se avaliar o efeito de diferentes nÃveis de fibra em detergente neutro (FDN) nas raÃÃes de frangas de duas linhagens comerciais de aves de postura, no perÃodo de 7 a 17 semanas de idade, sobre a curva de crescimento corporal e Ãssea e a deposiÃÃo de componentes na carcaÃa e nos ossos. Foram utilizadas 648 aves de cada linhagem, distribuÃdas em um delineamento experimental inteiramente casualizado, em esquema fatorial 3 x 2, composto de trÃs nÃveis de FDN (14,5; 16,5 e 18,5%) e duas linhagens (LOHMAN LSL e HY LINE BROWN), com quatro repetiÃÃes de 54 aves. Semanalmente, foram avaliados o peso corporal e das penas, peso e comprimento dos ossos (tÃbia e fÃmur) e a composiÃÃo corporal e dos ossos em proteÃna, cinzas e Ãgua. As curvas de crescimento e deposiÃÃo foram determinadas aplicando-se os dados na funÃÃo de Gompertz. NÃo houve interaÃÃo entre linhagem e nÃvel de FDN da raÃÃo, para os parÃmetros da equaÃÃo de Gompertz determinados, para todas as caracterÃsticas avaliadas. Os nÃveis de FDN da raÃÃo influenciaram significativamente nos parÃmetros da curva de crescimento para peso corporal e deposiÃÃo de Ãgua, de modo que o nÃvel de 14,5% de FDN possibilitou maior peso corporal e de deposiÃÃo de Ãgua à maturidade (Pm), maior idade de mÃximo crescimento (t*) e menor taxa de maturidade (b) que os demais nÃveis testados. Entretanto, os parÃmetros da curva de crescimento para o peso e o comprimento da tÃbia e do fÃmur, assim como, as estimativas dos parÃmetros para a deposiÃÃo de Ãgua nos ossos e as deposiÃÃes de proteÃna e matÃria mineral na carcaÃa e nos osso nÃo foram influencias significativamente pelo nÃvel de FDN da raÃÃo. Entre as linhagem, observou-se que as aves leves, apresentaram menor taxa de maturidade (b) e menor peso à maturidade (Pm), sem apresentar diferenÃas significativas na idade de mÃximo crescimento (t*). Os parÃmetros para a deposiÃÃo de proteÃna e cinzas na carcaÃa nÃo variaram significativamente, enquanto, as aves leves apresentaram menores estimativas de taxa de maturidade (b) para a deposiÃÃo de Ãgua corporal em relaÃÃo Ãs aves semipesadas. NÃo houve diferenÃa entre as linhagens para os parÃmetros estimados para o comprimento da tÃbia e do fÃmur, peso da tÃbia, deposiÃÃo de proteÃna e cinzas da tÃbia. Entretanto, para o peso do fÃmur, deposiÃÃo de proteÃna no fÃmur e deposiÃÃo de Ãgua na tÃbia, as aves leves apresentaram maior peso à maturidade (Pm) e valor da idade de mÃximo crescimento (t*) e menor valor na taxa de maturidade (b) em comparaÃÃo as aves semipesada, as quais apresentaram maior peso à maturidade (Pm) e valor da idade de mÃximo crescimento (t*) e menor valor na taxa de maturidade (b) em comparaÃÃo as aves leves para deposiÃÃo de Ãgua no fÃmur. Assim, o nÃvel de FDN da raÃÃo de recria pode ser utilizado para modificar a curva de crescimento das frangas leves e semipesadas, podendo-se controlar o ganho de peso corporal pelo aumento do seu nÃvel na raÃÃo em nÃvel superior a 14,5%, sem alterar o crescimento dos ossos e a deposiÃÃo de Ãgua, matÃria mineral e proteÃna na carcaÃa e nos ossos atà o nÃvel de 18,5%. Embora as poedeiras semipesadas da linhagem avaliada apresentem maior potencial de crescimento corporal e das penas em relaÃÃo Ãs leves, essa aves sÃo semelhantes quanto à proporÃÃo de proteÃna e matÃria mineral depositada na carcaÃa e divergem no desenvolvimento dos ossos quanto ao peso e deposiÃÃo de Ãgua e proteÃna no fÃmur. / The objective was to evaluate the effect of using different levels of neutral detergent fiber (NDF) in diets for hens of two commercial layer-hen strains from 7 to 17 weeks of age on the growth curve and deposition of body components and bones. A total of 648 birds from each strain were distributed in a completely randomized design in a 3 à 2 factorial arrangement consisting of three levels of NDF and two strains, with four replicates of 54 birds. The tested NDF levels were 14.5, 16.5 and 18.5%. Additionally, live weight, feather weight, body composition of protein, ash and water, bones weight, bones length and bones composition of protein, ash and water were evaluated. Growth curves were determined by applying the data on Gompertz function. According to the results, there was no interaction among factors, strain and NDF levels for the parameters of the equation of Gompertz determined for all evaluated traits. The NDF levels of the diet affected the estimates of weight at maturity and water deposition in the carcass. The level of 14.5% NDF allowed for greater weight at maturity (Wm), greater age at maximum growth (t*) and lower maturity rate (b) than the other tested levels. There was no influence of NDF levels tested on the parameters of the growth curve for weight and length of the tibia and femur (P <0.05). There was no influence of NDF levels tested on the estimates of the parameters of the Gompertz equation for the composition of water, protein and ash of the tibia and fÃmur (P <0.05). The level of NDF in the ration of growing can be used to modify the growth curve of pullets, being able to control the body weight gain by increasing its level in the ration without changing the deposition of water, ash and protein in the carcass. Pullets fed diets containing up to 18.5% inclusion of NDF, during 7-17 weeks of age, showed no changes in the curves of growth and nutrient deposition in the tibia and femur.

This study examines differences and similarities in how two animal ethicists living in different times have argued for a liberation of the animals, the basis for the study is Lewis Gompertz Moral Inquiries: On the Situation of Man and of Brutes (1824) and Peter Singers Animal Liberation (1975). The analysis has been conducted with a historical perspective where close reading and contextualization have been used to further understand both the sources and the authors. The investigation is limited to four themes: animal's ability to experience, to kill animals, using animals and products of animals, and finally the idea of equality. The study concludes that there are significant similarities between the arguments Gompertz and Singer use, and that their ideas are rooted in a view of equality where the ability to suffer and have needs should be fundamental for our moral caring towards other creatures. A significant difference between the authors is their relationship to reason, where Gompertz highlights the animals' ability to reason as a cause to treat them well while Singer dismisses the idea that such abilities are of any interest for our moral considerations. The study also points out that the differences in the authors' conclusions and arguments can be understood on the basis of the scientific and intellectual context they operate in, where Gompertz can be described as an enlightenment philosopher with a strong belief in the developable reason within creatures, while the modern-day philosopher Singer rather sees reason as excluding, not only of animals but also of human beings. For animals to be liberated from man's oppression, both writers argue that it is necessary for man to eat a vegetarian diet.

Este estudio tiene como objetivo evaluar el futuro de los casos confirmados de Covid-19 en el Perú, utilizando el modelo de regresión no lineal de Gompertz. Los datos utilizados están basados en los informes oficiales del Ministerio de Salud del Perú (MINSA). El valor acumulado de casos fatales fue sometido a un análisis interactivo por el método de mínimos cuadrados no lineales para proyectar el modelo. A partir de la derivada de primer orden del modelo predictivo fue obtenido la curva de casos fatales diarios. Usando la tasa de letalidad como proporción entre infectados y casos fatales, además del desfase promedio de días entre estos, fue posible estimar la curva epidémica. Por el momento, el modelo predictivo sugiere que el Perú estaría en un descenso lento de la curva epidémica, distanciandose del pico de contagios por día. Asimismo, se observó una tendencia de alcanzar unos 550 mil infectados y unos 19 mil fallecidos hasta fines del año 2020. Las predicciones de los modelos matemáticos pueden variar con la actualización periódica de datos, predicciones actualizadas serán publicadas en www.yupay-dynamic.com

No description available.

Sigmoid curves have found broad applicability in biological sciences and biopharmaceutical research during the last decades. A well planned experiment design is essential to accurately estimate the parameters of the model. In contrast to a large literature and extensive results on optimal designs for linear models, research on the design for nonlinear, including sigmoid curve, models has not kept pace. Furthermore, most of the work in the optimal design literature for nonlinear models concerns the characterization of minimally supported designs. These minimal, optimal designs are frequently criticized for their inability to check goodness of fit, as there are no additional degrees of freedom for the testing. This design issue can be a serious problem, since checking the model adequacy is of particular importance when the model is selected without complete certainty. To assess for lack of fit, we must add at least one extra distinct design point to the experiment. The goal of this dissertation is to identify optimal or highly efficient designs capable of checking the fit for sigmoid curve models. In this dissertation, we consider some commonly used sigmoid curves, including logistic, probit and Gompertz models with two, three, or four parameters. We use D-optimality as our design criterion. We first consider adding one extra point to the design, and consider five alternative designs and discuss their suitability to test for lack of fit. Then we extend the results to include one more additional point to better understand the compromise among the need of detecting lack of fit, maintaining high efficiency and the practical convenience for the practitioners. We then focus on the two-parameter Gompertz model, which is widely used in fitting growth curves yet less studied in literature, and explore three-point designs for testing lack of fit under various error variance structures. One reason that nonlinear design problems are so challenging is that, with nonlinear models, information matrices and optimal designs depend on the unknown model parameters. We propose a strategy to bypass the obstacle of parameter dependence for the theoretical derivation. This dissertation also successfully characterizes many commonly studied sigmoid curves in a generalized way by imposing unified parameterization conditions, which can be generalized and applied in the studies of other sigmoid curves. We also discuss Gompertz model with different error structures in finding an extra point for testing lack of fit. / Statistics