Monitoring Infection Risk for Air and Soil Borne Fungal Plant Pathogens using Antibody and DNA Techniques and Mathematical Models describing Environmental Parameters

Economic losses resulting from disease development can be reduced by accurate and early detection of plant pathogens. Early detection can provide the grower with useful information on optimal crop rotation patterns, varietal selections, appropriate control measures, harvest date and post harvest handling. Classical methods for the isolation of pathogens are commonly used only after disease symptoms. This frequently results in a delay in application of control measures at potentially important periods in crop production. This paper describes the application of both antibody and DNA based systems to monitor infection risk of air and soil borne fungal pathogens and the use of this information with mathematical models describing risk of disease associated with environmental parameters.

Applying Mathematical Models to Study the Role of the Immune System in Chronic Myelogenous Leukemia

Although tyrosine kinase inhibitors (TKIs) such as imatinib have transformed chronic myelogenous leukemia (CML) into a chronic condition, these therapies are not curative in the majority of cases. Most patients must continue TKI therapy indefinitely, a requirement that is both expensive and that compromises a patient's quality of life. While TKIs are known to reduce leukemic cells' proliferative capacity and to induce apoptosis, their effects on leukemic stem cells, the immune system, and the microenvironment are not fully understood. A more complete understanding of their global therapeutic effects would help us to identify any limitations of TKI monotherapy and to address these issues through novel combination therapies. Mathematical models are a complementary tool to experimental and clinical data that can provide valuable insights into the underlying mechanisms of TKI therapy. Previous modeling efforts have focused on CML patients who show biphasic and triphasic exponential declines in BCR-ABL ratio during therapy. However, our patient data indicates that many patients treated with TKIs show fluctuations in BCR-ABL ratio yet are able to achieve durable remissions. To investigate these fluctuations, we construct a mathematical model that integrates CML with a patient's autologous immune response to the disease. In our model, we define an immune window, which is an intermediate range of leukemic concentrations that lead to an effective immune response against CML. While small leukemic concentrations provide insufficient stimulus, large leukemic concentrations actively suppress a patient's immune system, thus limiting it's ability to respond. Our patient data and modeling results suggest that at diagnosis, a patient's high leukemic concentration is able to suppress their immune system. TKI therapy drives the leukemic population into the immune window, allowing the patient's immune cells to expand and eventually mount an efficient response against the residual CML. This response drives the leukemic population below the immune window, causing the immune population to contract and allowing the leukemia to partially recover. The leukemia eventually reenters the immune window, thus stimulating a sequence of weaker immune responses as the two populations approach equilibrium. We hypothesize that a patient's autologous immune response to CML may explain the fluctuations in BCR-ABL ratio that are regularly seen during TKI therapy. These fluctuations may serve as a signature of a patient's individual immune response to CML. By applying our modeling framework to patient data, we are able to construct an immune profile that can then be used to propose patient-specific combination therapies aimed at further reducing a patient's leukemic burden. Our characterization of a patient's anti-leukemia immune response may be especially valuable in the study of drug resistance, treatment cessation, and combination therapy.

Application of mathematical models to mycotoxins children risk assessment: a case study of Portuguese children exposure to co-occurring mycotoxins in processed cereal-based foods

People, animals and the environment can be exposed to multiple chemicals at once from a variety of sources, but current risk assessment is usually carried out based on one chemical substance at a time. In human health risk assessment, ingestion of food is considered a major route of exposure to many contaminants, namely mycotoxins, a wide group of fungal secondary metabolites that are known to potentially cause toxicity and carcinogenic outcomes. Mycotoxins are commonly found in a variety of foods including those intended for consumption by infants and young children and have been found in processed cereal-based foods available in the Portuguese market. The use of mathematical models, including probabilistic approaches using Monte Carlo simulations, constitutes a prominent issue in human health risk assessment in general and in mycotoxins exposure assessment in particular. The present study aims to characterize, for the first time, the risk associated with the exposure of Portuguese children to single and multiple mycotoxins present in processed cereal-based foods (CBF). Portuguese children (0-3 years old) food consumption data (n=103) were collected using a 3 days food diary. Contamination data concerned the quantification of 12 mycotoxins (aflatoxins, ochratoxin A, fumonisins and trichothecenes) were evaluated in 20 CBF samples marketed in 2014 and 2015 in Lisbon; samples were analyzed by HPLC-FLD, LC-MS/MS and GC-MS. Daily exposure of children to mycotoxins was performed using deterministic and probabilistic approaches. Different strategies were used to treat the left censored data. For aflatoxins, as carcinogenic compounds, the margin of exposure (MoE) was calculated as a ratio of BMDL (benchmark dose lower confidence limit) to the aflatoxin exposure. The magnitude of the MoE gives an indication of the risk level. For the remaining mycotoxins, the output of exposure was compared to the dose reference values (TDI) in order to calculate the hazard quotients (ratio between exposure and a reference dose, HQ). For the cumulative risk assessment of multiple mycotoxins, the concentration addition (CA) concept was used. The combined margin of exposure (MoET) and the hazard index (HI) were calculated for aflatoxins and the remaining mycotoxins, respectively. 71% of CBF analyzed samples were contaminated with mycotoxins (with values below the legal limits) and approximately 56% of the studied children consumed CBF at least once in these 3 days. Preliminary results showed that children exposure to single mycotoxins present in CBF were below the TDI. Aflatoxins MoE and MoET revealed a reduced potential risk by exposure through consumption of CBF (with values around 10000 or more). HQ and HI values for the remaining mycotoxins were below 1. Children are a particularly vulnerable population group to food contaminants and the present results point out an urgent need to establish legal limits and control strategies regarding the presence of multiple mycotoxins in children foods in order to protect their health. The development of packaging materials with antifungal properties is a possible solution to control the growth of moulds and consequently to reduce mycotoxin production, contributing to guarantee the quality and safety of foods intended for children consumption.

An introduction to mathematical models of coagulation-fragmentation processes: a discrete deterministic mean-field approach

We summarise the properties and the fundamental mathematical results associated with basic models which describe coagulation and fragmentation processes in a deterministic manner and in which cluster size is a discrete quantity (an integer multiple of some basic unit size). In particular, we discuss Smoluchowski's equation for aggregation, the Becker-Döring model of simultaneous aggregation and fragmentation, and more general models involving coagulation and fragmentation.

Chebanov law and Vakar formula in mathematical models of complex systems

Ecological models written in a mathematical language L(M) or model language, with a given style or methodology can be considered as a text. It is possible to apply statistical linguistic laws and the experimental results demonstrate that the behaviour of a mathematical model is the same of any literary text of any natural language. A text has the following characteristics: (a) the variables, its transformed functions and parameters are the lexic units or LUN of ecological models; (b) the syllables are constituted by a LUN, or a chain of them, separated by operating or ordering LUNs; (c) the flow equations are words; and (d) the distribution of words (LUM and CLUN) according to their lengths is based on a Poisson distribution, the Chebanov's law. It is founded on Vakar's formula, that is calculated likewise the linguistic entropy for L(M). We will apply these ideas over practical examples using MARIOLA model. In this paper it will be studied the problem of the lengths of the simple lexic units composed lexic units and words of text models, expressing these lengths in number of the primitive symbols, and syllables. The use of these linguistic laws renders it possible to indicate the degree of information given by an ecological model.

Mathematical models for cellular aggregation: the chemotactic instability and clustering formation

In this thesis we present a mathematical formulation of the interaction between microorganisms such as bacteria or amoebae and chemicals, often produced by the organisms themselves. This interaction is called chemotaxis and leads to cellular aggregation. We derive some models to describe chemotaxis. The first is the pioneristic Keller-Segel parabolic-parabolic model and it is derived by two different frameworks: a macroscopic perspective and a microscopic perspective, in which we start with a stochastic differential equation and we perform a mean-field approximation. This parabolic model may be generalized by the introduction of a degenerate diffusion parameter, which depends on the density itself via a power law. Then we derive a model for chemotaxis based on Cattaneo's law of heat propagation with finite speed, which is a hyperbolic model. The last model proposed here is a hydrodynamic model, which takes into account the inertia of the system by a friction force. In the limit of strong friction, the model reduces to the parabolic model, whereas in the limit of weak friction, we recover a hyperbolic model. Finally, we analyze the instability condition, which is the condition that leads to aggregation, and we describe the different kinds of aggregates we may obtain: the parabolic models lead to clusters or peaks whereas the hyperbolic models lead to the formation of network patterns or filaments. Moreover, we discuss the analogy between bacterial colonies and self gravitating systems by comparing the chemotactic collapse and the gravitational collapse (Jeans instability).

Models of blast furnaces for smelting iron / by Henry W. Nichols, Assoc. Curator of Geology.

no.2(1922)

In silico pathway reconstruction: Iron-sulfur cluster biogenesis in Saccharomyces cerevisiae

Background: Current advances in genomics, proteomics and other areas of molecular biology make the identification and reconstruction of novel pathways an emerging area of great interest. One such class of pathways is involved in the biogenesis of Iron-Sulfur Clusters (ISC). Results: Our goal is the development of a new approach based on the use and combination of mathematical, theoretical and computational methods to identify the topology of a target network. In this approach, mathematical models play a central role for the evaluation of the alternative network structures that arise from literature data-mining, phylogenetic profiling, structural methods, and human curation. As a test case, we reconstruct the topology of the reaction and regulatory network for the mitochondrial ISC biogenesis pathway in S. cerevisiae. Predictions regarding how proteins act in ISC biogenesis are validated by comparison with published experimental results. For example, the predicted role of Arh1 and Yah1 and some of the interactions we predict for Grx5 both matches experimental evidence. A putative role for frataxin in directly regulating mitochondrial iron import is discarded from our analysis, which agrees with also published experimental results. Additionally, we propose a number of experiments for testing other predictions and further improve the identification of the network structure. Conclusion: We propose and apply an iterative in silico procedure for predictive reconstruction of the network topology of metabolic pathways. The procedure combines structural bioinformatics tools and mathematical modeling techniques that allow the reconstruction of biochemical networks. Using the Iron Sulfur cluster biogenesis in S. cerevisiae as a test case we indicate how this procedure can be used to analyze and validate the network model against experimental results. Critical evaluation of the obtained results through this procedure allows devising new wet lab experiments to confirm its predictions or provide alternative explanations for further improving the models.

Mathematical modeling and optimal control of malaria

Malaria continues to infect millions and kill hundreds of thousands of people worldwide each year, despite over a century of research and attempts to control and eliminate this infectious disease. Challenges such as the development and spread of drug resistant malaria parasites, insecticide resistance to mosquitoes, climate change, the presence of individuals with subpatent malaria infections which normally are asymptomatic and behavioral plasticity in the mosquito hinder the prospects of malaria control and elimination. In this thesis, mathematical models of malaria transmission and control that address the role of drug resistance, immunity, iron supplementation and anemia, immigration and visitation, and the presence of asymptomatic carriers in malaria transmission are developed. A within-host mathematical model of severe Plasmodium falciparum malaria is also developed. First, a deterministic mathematical model for transmission of antimalarial drug resistance parasites with superinfection is developed and analyzed. The possibility of increase in the risk of superinfection due to iron supplementation and fortification in malaria endemic areas is discussed. The model results calls upon stakeholders to weigh the pros and cons of iron supplementation to individuals living in malaria endemic regions. Second, a deterministic model of transmission of drug resistant malaria parasites, including the inflow of infective immigrants, is presented and analyzed. The optimal control theory is applied to this model to study the impact of various malaria and vector control strategies, such as screening of immigrants, treatment of drug-sensitive infections, treatment of drug-resistant infections, and the use of insecticide-treated bed nets and indoor spraying of mosquitoes. The results of the model emphasize the importance of using a combination of all four controls tools for effective malaria intervention. Next, a two-age-class mathematical model for malaria transmission with asymptomatic carriers is developed and analyzed. In development of this model, four possible control measures are analyzed: the use of long-lasting treated mosquito nets, indoor residual spraying, screening and treatment of symptomatic, and screening and treatment of asymptomatic individuals. The numerical results show that a disease-free equilibrium can be attained if all four control measures are used. A common pitfall for most epidemiological models is the absence of real data; model-based conclusions have to be drawn based on uncertain parameter values. In this thesis, an approach to study the robustness of optimal control solutions under such parameter uncertainty is presented. Numerical analysis of the optimal control problem in the presence of parameter uncertainty demonstrate the robustness of the optimal control approach that: when a comprehensive control strategy is used the main conclusions of the optimal control remain unchanged, even if inevitable variability remains in the control profiles. The results provide a promising framework for the design of cost-effective strategies for disease control with multiple interventions, even under considerable uncertainty of model parameters. Finally, a separate work modeling the within-host Plasmodium falciparum infection in humans is presented. The developed model allows re-infection of already-infected red blood cells. The model hypothesizes that in severe malaria due to parasite quest for survival and rapid multiplication, the Plasmodium falciparum can be absorbed in the already-infected red blood cells which accelerates the rupture rate and consequently cause anemia. Analysis of the model and parameter identifiability using Markov chain Monte Carlo methods is presented.

Modern mathematical methods and models; a book of experimental text materials.

v. 1. Multicomponent methods.--v. 2. Mathematical models.

Estudo de variabilidade e otimização do circuito de moagem SAG da Usina do Sossego

Sossego was the first Vale SAG mill operation to process copper-gold ore. It is located in the State of Para, southeastern Amazon region of Brazil. In the first three years of continuous operation, Vale investigated different alternatives for improving the circuit`s performance by investigating operating conditions, mainly focusing on the SAG mill. It was decided to further assess the performance of the comminution circuit as a function of ore characteristics. A comprehensive ore characterization program was then conducted, together with the calibration of mathematical models on the basis of surveys carried out at the industrial circuit. The simulator was then used to predict the throughput associated to each ore type, as well as to establish the optimized circuit configuration and tailored operating conditions. This paper describes in detail the main aspects of optimizing the industrial circuit performance, as well as the successful method for predicting the production as a function of ore characteristics and circuit configuration.

Modelling solute transport in structured soils: Performance evaluation of the ADR and TRM models

The movement of chemicals through the soil to the groundwater or discharged to surface waters represents a degradation of these resources. In many cases, serious human and stock health implications are associated with this form of pollution. The chemicals of interest include nutrients, pesticides, salts, and industrial wastes. Recent studies have shown that current models and methods do not adequately describe the leaching of nutrients through soil, often underestimating the risk of groundwater contamination by surface-applied chemicals, and overestimating the concentration of resident solutes. This inaccuracy results primarily from ignoring soil structure and nonequilibrium between soil constituents, water, and solutes. A multiple sample percolation system (MSPS), consisting of 25 individual collection wells, was constructed to study the effects of localized soil heterogeneities on the transport of nutrients (NO3-, Cl-, PO43-) in the vadose zone of an agricultural soil predominantly dominated by clay. Very significant variations in drainage patterns across a small spatial scale were observed tone-way ANOVA, p < 0.001) indicating considerable heterogeneity in water flow patterns and nutrient leaching. Using data collected from the multiple sample percolation experiments, this paper compares the performance of two mathematical models for predicting solute transport, the advective-dispersion model with a reaction term (ADR), and a two-region preferential flow model (TRM) suitable for modelling nonequilibrium transport. These results have implications for modelling solute transport and predicting nutrient loading on a larger scale. (C) 2001 Elsevier Science Ltd. All rights reserved.

Analysis of dynamic process models for structural insight and model reduction .1. Structural identification measures

An important consideration in the development of mathematical models for dynamic simulation, is the identification of the appropriate mathematical structure. By building models with an efficient structure which is devoid of redundancy, it is possible to create simple, accurate and functional models. This leads not only to efficient simulation, but to a deeper understanding of the important dynamic relationships within the process. In this paper, a method is proposed for systematic model development for startup and shutdown simulation which is based on the identification of the essential process structure. The key tool in this analysis is the method of nonlinear perturbations for structural identification and model reduction. Starting from a detailed mathematical process description both singular and regular structural perturbations are detected. These techniques are then used to give insight into the system structure and where appropriate to eliminate superfluous model equations or reduce them to other forms. This process retains the ability to interpret the reduced order model in terms of the physico-chemical phenomena. Using this model reduction technique it is possible to attribute observable dynamics to particular unit operations within the process. This relationship then highlights the unit operations which must be accurately modelled in order to develop a robust plant model. The technique generates detailed insight into the dynamic structure of the models providing a basis for system re-design and dynamic analysis. The technique is illustrated on the modelling for an evaporator startup. Copyright (C) 1996 Elsevier Science Ltd

Mathematical modelling of supercritical CO2 extraction of volatile oils from aromatic plants

The modelling of the experimental data of the extraction of the volatile oil from six aromatic plants (coriander, fennel, savoury, winter savoury, cotton lavender and thyme) was performed using five mathematical models, based on differential mass balances. In all cases the extraction was internal diffusion controlled and the internal mass transfer coefficienty (k(s)) have been found to change with pressure, temperature and particle size. For fennel, savoury and cotton lavender, the external mass transfer and the equilibrium phase also influenced the second extraction period, since k(s) changed with the tested flow rates. In general, the axial dispersion coefficient could be neglected for the conditions studied, since Peclet numbers were high. On the other hand, the solute-matrix interaction had to be considered in order to ensure a satisfactory description of the experimental data.

A mathematical model for malaria transmission relating global warming and local socioeconomic conditions

OBJECTIVE: Sensitivity analysis was applied to a mathematical model describing malaria transmission relating global warming and local socioeconomic conditions. METHODS: A previous compartment model was proposed to describe the overall transmission of malaria. This model was built up on several parameters and the prevalence of malaria in a community was characterized by the values assigned to them. To assess the control efforts, the model parameters can vary on broad intervals. RESULTS: By performing the sensitivity analysis on equilibrium points, which represent the level of malaria infection in a community, the different possible scenarios are obtained when the parameters are changed. CONCLUSIONS: Depending on malaria risk, the efforts to control its transmission can be guided by a subset of parameters used in the mathematical model.