Dermic diffusion and stratum corneum: a state of the art review of mathematical models

Transdermal biotechnologies are an ever increasing field of interest, due to the medical and pharmaceutical applications that they underlie. There are several mathematical models at use that permit a more inclusive vision of pure experimental data and even allow practical extrapolation for new dermal diffusion methodologies. However, they grasp a complex variety of theories and assumptions that allocate their use for specific situations. Models based on Fick's First Law found better use in contexts where scaled particle theory Models would be extensive in time-span but the reciprocal is also true, as context of transdermal diffusion of particular active compounds changes. This article reviews extensively the various theoretical methodologies for studying dermic diffusion in the rate limiting dermic barrier, the stratum corneum, and systematizes its characteristics, their proper context of application, advantages and limitations, as well as future perspectives.

New findings on the dynamics of HIV and TB coinfection models

In this paper we study a model for HIV and TB coinfection. We consider the integer order and the fractional order versions of the model. Let α∈[0.78,1.0] be the order of the fractional derivative, then the integer order model is obtained for α=1.0. The model includes vertical transmission for HIV and treatment for both diseases. We compute the reproduction number of the integer order model and HIV and TB submodels, and the stability of the disease free equilibrium. We sketch the bifurcation diagrams of the integer order model, for variation of the average number of sexual partners per person and per unit time, and the tuberculosis transmission rate. We analyze numerical results of the fractional order model for different values of α, including α=1. The results show distinct types of transients, for variation of α. Moreover, we speculate, from observation of the numerical results, that the order of the fractional derivative may behave as a bifurcation parameter for the model. We conclude that the dynamics of the integer and the fractional order versions of the model are very rich and that together these versions may provide a better understanding of the dynamics of HIV and TB coinfection.

Soil sampling design and sampling techniques for soil properties monitoring – common difficulties related to forest soils

Mathematical models and statistical analysis are key instruments in soil science scientific research as they can describe and/or predict the current state of a soil system. These tools allow us to explore the behavior of soil related processes and properties as well as to generate new hypotheses for future experimentation. A good model and analysis of soil properties variations, that permit us to extract suitable conclusions and estimating spatially correlated variables at unsampled locations, is clearly dependent on the amount and quality of data and of the robustness techniques and estimators. On the other hand, the quality of data is obviously dependent from a competent data collection procedure and from a capable laboratory analytical work. Following the standard soil sampling protocols available, soil samples should be collected according to key points such as a convenient spatial scale, landscape homogeneity (or non-homogeneity), land color, soil texture, land slope, land solar exposition. Obtaining good quality data from forest soils is predictably expensive as it is labor intensive and demands many manpower and equipment both in field work and in laboratory analysis. Also, the sampling collection scheme that should be used on a data collection procedure in forest field is not simple to design as the sampling strategies chosen are strongly dependent on soil taxonomy. In fact, a sampling grid will not be able to be followed if rocks at the predicted collecting depth are found, or no soil at all is found, or large trees bar the soil collection. Considering this, a proficient design of a soil data sampling campaign in forest field is not always a simple process and sometimes represents a truly huge challenge. In this work, we present some difficulties that have occurred during two experiments on forest soil that were conducted in order to study the spatial variation of some soil physical-chemical properties. Two different sampling protocols were considered for monitoring two types of forest soils located in NW Portugal: umbric regosol and lithosol. Two different equipments for sampling collection were also used: a manual auger and a shovel. Both scenarios were analyzed and the results achieved have allowed us to consider that monitoring forest soil in order to do some mathematical and statistical investigations needs a sampling procedure to data collection compatible to established protocols but a pre-defined grid assumption often fail when the variability of the soil property is not uniform in space. In this case, sampling grid should be conveniently adapted from one part of the landscape to another and this fact should be taken into consideration of a mathematical procedure.

Mathematical model for HIV dynamics in HIV-specific helper cells

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4 + T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4 + T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and; (2) virus production period for new virions to be produced within and released from the infected cells. We compute the reproduction number of the model, R0, and the local stability of the disease free equilibrium and of the endemic equilibrium. We find that for values of R0<1, the model approaches asymptotically the disease free equilibrium. For values of R0>1, the model approximates asymptotically the endemic equilibrium. We observe numerically the phenomenon of backward bifurcation for values of R0⪅1. This statement will be proved in future work. We also vary the values of the latent period and the production period of infected cells and free virus. We conclude that increasing these values translates in a decrease of the reproduction number. Thus, a good strategy to control the HIV virus should focus on drugs to prolong the latent period and/or slow down the virus production. These results suggest that the model is mathematically and epidemiologically well-posed.

Effects of treatment, awareness and condom use in a coinfection model for HIV and HCV in MSM

We develop a new a coinfection model for hepatitis C virus (HCV) and the human immunodeficiency virus (HIV). We consider treatment for both diseases, screening, unawareness and awareness of HIV infection, and the use of condoms. We study the local stability of the disease-free equilibria for the full model and for the two submodels (HCV only and HIV only submodels). We sketch bifurcation diagrams for different parameters, such as the probabilities that a contact will result in a HIV or an HCV infection. We present numerical simulations of the full model where the HIV, HCV and double endemic equilibria can be observed. We also show numerically the qualitative changes of the dynamical behavior of the full model for variation of relevant parameters. We extrapolate the results from the model for actual measures that could be implemented in order to reduce the number of infected individuals.

Viabilidade Técnica e Económica das Diferentes Tecnologias de Microprodução

Sabendo que as energias de origem fóssil não são inesgotáveis e que afetam a qualidade do ambiente, nos últimos anos, o interesse pelas energias renováveis mereceu a atenção de ambientalistas e de governantes. Para diminuir a importação de energia, o próprio governo de Portugal incentivou, através de medidas legislativas diversas, a instalação de sistemas alternativos de produção elétrica. Face à pertinência desta matéria, a dissertação, Viabilidade Técnica e Económica das Diferentes Tecnologias de Microprodução, aborda o aproveitamento de energias renováveis através de tecnologias de Microprodução ligadas à rede elétrica. Nesta dissertação, numa primeira fase, apresentam-se os sistemas de microprodução existentes no mercado, descrevem-se os componentes que os constituem e destacam-se os aspetos legislativos aplicáveis. Numa segunda fase, com o objetivo de suportar a elaboração de uma ferramenta informática para apoio na escolha de equipamentos de microprodução, procede-se à análise financeira de tecnologias de microprodução, indicando os modelos matemáticos necessários. Um dos objetivos da dissertação, consiste na construção de uma ferramenta informática de cálculo e na sua aplicação a dois estudos de caso. Esse programa informático foi elaborado em Excel e é capaz de fornecer uma estimativa da produção de energia anual e da avaliação da viabilidade técnico-económica de cada tecnologia e pretende apoiar a decisão do investidor em tecnologias de microprodução. Tendo sido realizados dois estudos de caso - um edifício habitacional unifamiliar e um edifício Industrial – foi possível verificar o funcionamento da aplicação e a sua utilidade na determinação da solução mais vantajosa na escolha de uma tecnologia de microprodução, uma vez que, introduzidos os dados adequados, são gerados os cálculos que permitem fornecer uma visão de conjunto, possibilitando a comparação das diferentes propostas.