Data surveillance for infectious diseases: models, complex networks and machine learning

In this thesis, we investigate the role of applied physics in epidemiological surveillance through the application of mathematical models, network science and machine learning. The spread of a communicable disease depends on many biological, social, and health factors. The large masses of data available make it possible, on the one hand, to monitor the evolution and spread of pathogenic organisms; on the other hand, to study the behavior of people, their opinions and habits. Presented here are three lines of research in which an attempt was made to solve real epidemiological problems through data analysis and the use of statistical and mathematical models. In Chapter 1, we applied language-inspired Deep Learning models to transform influenza protein sequences into vectors encoding their information content. We then attempted to reconstruct the antigenic properties of different viral strains using regression models and to identify the mutations responsible for vaccine escape. In Chapter 2, we constructed a compartmental model to describe the spread of a bacterium within a hospital ward. The model was informed and validated on time series of clinical measurements, and a sensitivity analysis was used to assess the impact of different control measures. Finally (Chapter 3) we reconstructed the network of retweets among COVID-19 themed Twitter users in the early months of the SARS-CoV-2 pandemic. By means of community detection algorithms and centrality measures, we characterized users’ attention shifts in the network, showing that scientific communities, initially the most retweeted, lost influence over time to national political communities. In the Conclusion, we highlighted the importance of the work done in light of the main contemporary challenges for epidemiological surveillance. In particular, we present reflections on the importance of nowcasting and forecasting, the relationship between data and scientific research, and the need to unite the different scales of epidemiological surveillance.

Failure detection for transport processes on networks

Diffusion on networks is a convenient framework to describe transport systems of different nature (from biological transport systems to urban mobility). The mathematical models are based on master equations that describe the diffusion processes by means of the weighted Laplacian matrix that connects the nodes. The link weight represent the coupling strength between the nodes. In this thesis we cope with the problem of localizing a single-edge failure that occurs in the network. An edge failure is meant to be as a sudden decrease of its transport capacities. An incomplete observation of the dynamical state of the network is available. An optimal clustering procedure based on the correlation properties among the node states is proposed. The network dimensionality is then reduced introducing representative nodes for each cluster, whose dynamical state is observed. We check the efficiency of the failure localization for our clustering method in comparison with more traditional techniques, using different graph configurations.

A method to lower the detection limit for optical beat signals from a frequency-dithered stabilized laser

A narrow absorption feature in an atomic or molecular gas (such as iodine or methane) is used as the frequency reference in many stabilized lasers. As part of the stabilization scheme an optical frequency dither is applied to the laser. In optical heterodyne experiments, this dither is transferred to the RF beat signal, reducing the spectral power density and hence the signal to noise ratio over that in the absence of dither. We removed the dither by mixing the raw beat signal with a dithered local oscillator signal. When the dither waveform is matched to that of the reference laser the output signal from the mixer is rendered dither free. Application of this method to a Winters iodine-stabilized helium-neon laser reduced the bandwidth of the beat signal from 6 MHz to 390 kHz, thereby lowering the detection threshold from 5 pW of laser power to 3 pW. In addition, a simple signal detection model is developed which predicts similar threshold reductions.

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

Detection of TGIF1 homeobox gene in oral squamous cell carcinoma according to histologic grading

Objective. TGIF1 homeobox gene involvement in oral cancer has not yet been investigated. This study analyzed the expression of TGIF1 transcripts and protein in oral squamous cell carcinoma (OSCC). Study design. Snap-frozen samples from 16 patients were taken from both OSCC and nontumoral adjacent epithelium (NT) for in situ hybridization (ISH). Forty-six paraffin-embedded samples of OSCC were submitted to immunohistochemistry (IHC). A descriptive analysis of the transcript signal detection was accomplished, and TGIF1 immunoexpression was carried out considering protein levels, localization, and cellular differentiation. Results. ISH reactions showed TGIF1 transcripts with a signal that was frequently intense in NT, and generally weak in OSCC, and that had stronger transcript signal in well-differentiated areas of OSCC when compared with poorly differentiated ones. IHC reactions had poorly differentiated cases associated with TGIF1 protein expression in both the nucleus and cytoplasm (P = .05, Fisher test). Conclusions. TGIF1 gain or loss of function might possibly play a role in oral cancer cell differentiation. (Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2011; 111: 218-224)

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.

Analysis of glycosylation heterogeneity in antibody production by Pichia pastoris

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Biotecnologia

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.

A new, automated, four-colour interphase FISH approach for the simultaneous detection of specific aneuploidies of diagnosis and prognosis significance in high hyperdiploid ALL

In hyperdiploid acute lymphoblastic leukaemia (ALL), the simultaneous occurrence of specific aneuploidies confers a more favourable outcome than hyperdiploidy alone. Interphase (I) FISH complements conventional cytogenetics (CC) through its sensitivity and ability to detect chromosome aberrations in non-dividing cells. To overcome the limits of manual I-FISH, we developed an automated four-colour I-FISH approach and assessed its ability to detect concurrent aneuploidies in ALL. I-FISH was performed using centromeric probes for chromosomes 4, 6, 10 and 17. Parameters established for automatic nucleus selection and signal detection were evaluated (3 controls). Cut-off values were determined (10 controls, 1000 nuclei/case). Combinations of aneuploidies were considered relevant when each aneuploidy was individually significant. Results obtained in 10 ALL patients (1500 nuclei/patient) were compared with those by CC. Various combinations of aneuploidies were identified. All clones detected by CC were observed by I-FISH. I-FISH revealed numerous additional abnormal clones, ranging between 0.1 % and 31.6%, based on the large number of nuclei evaluated. Four-colour automated I-FISH permits the identification of concurrent aneuploidies of prognostic significance in hyperdiploid ALL. Large numbers of cells can be analysed rapidly by this method. Owing to its high sensitivity, the method provides a powerful tool for the detection of small abnormal clones at diagnosis and during follow up. Compared to CC, it generates a more detailed cytogenetic picture, the biological and clinical significance of which merits further evaluation. Once optimised for a given set of probes, the system can be easily adapted for other probe combinations.

Automated four-color interphase fluorescence in situ hybridization approach for the simultaneous detection of specific aneuploidies of diagnostic and prognostic significance in high hyperdiploid acute lymphoblastic leukemia.

In high hyperdiploid acute lymphoblastic leukemia (ALL), the concurrence of specific trisomies confers a more favorable outcome than hyperdiploidy alone. Interphase fluorescence in situ hybridization (FISH) complements conventional cytogenetics (CC) through its sensitivity and ability to detect chromosome aberrations in nondividing cells. To overcome the limits of manual I-FISH, we developed an automated four-color I-FISH approach and assessed its ability to detect concurrent aneuploidies in ALL. I-FISH was performed using centromeric probes for chromosomes 4, 6, 10, and 17. Parameters established for nucleus selection and signal detection were evaluated. Cutoff values were determined. Combinations of aneuploidies were considered relevant when each aneuploidy was individually significant. Results obtained in 10 patient samples were compared with those obtained with CC. Various combinations of aneuploidies were identified. All clones detected by CC were observed also by I-FISH, and I-FISH revealed numerous additional abnormal clones in all patients, ranging from < or =1% to 31.6% of cells analyzed. We conclude that four-color automated I-FISH permits the identification of concurrent aneuploidies of potential prognostic significance. Large numbers of cells can be analyzed rapidly. The large number of nuclei scored revealed a high level of chromosome variability both at diagnosis and relapse, the prognostic significance of which is of considerable clinical interest and merits further evaluation.

Epidemic models with an infected-infectious period

The introduction of an infective-infectious period on the geographic spread of epidemics is considered in two different models. The classical evolution equations arising in the literature are generalized and the existence of epidemic wave fronts is revised. The asymptotic speed is obtained and improves previous results for the Black Death plague

A new, automated, four-colour interphase FISH approach for the simultaneous detection of specific aneuploidies of diagnostic and prognostic significance in high hyperdiploid ALL

In hyperdiploid acute lymphoblastic leukaemia (ALL), the simultaneous occurrence of specific aneuploidies confers a more favourable outcome than hyperdiploidy alone. Interphase (I) FISH complements conventional cytogenetics (CC) through its sensitivity and ability to detect chromosome aberrations in non-dividing cells. To overcome the limits of manual I-FISH, we developed an automated four-colour I-FISH approach and assessed its ability to detect concurrent aneuploidies in ALL. I-FISH was performed using centromeric probes for chromosomes 4, 6, 10 and 17. Parameters established for automatic nucleus selection and signal detection were evaluated (3 controls). Cut-off values were determined (10 controls, 1000 nuclei/case). Combinations of aneuploidies were considered relevant when each aneuploidy was individually significant. Results obtained in 10 ALL patients (1500 nuclei/patient) were compared with those by CC. Various combinations of aneuploidies were identified. All clones detected by CC were observed by I-FISH. I-FISH revealed numerous additional abnormal clones, ranging between 0.1% and 31.6%, based on the large number of nuclei evaluated. Four-colour automated I-FISH permits the identification of concurrent aneuploidies of prognostic significance in hyperdiploid ALL. Large numbers of cells can be analysed rapidly by this method. Owing to its high sensitivity, the method provides a powerful tool for the detection of small abnormal clones at diagnosis and during follow up. Compared to CC, it generates a more detailed cytogenetic picture, the biological and clinical significance of which merits further evaluation. Once optimised for a given set of probes, the system can be easily adapted for other probe combinations.

Estimation of the parameters of the gravitational-wage signal of a coalescing binary system

The statistical theory of signal detection and the estimation of its parameters are reviewed and applied to the case of detection of the gravitational-wave signal from a coalescing binary by a laser interferometer. The correlation integral and the covariance matrix for all possible static configurations are investigated numerically. Approximate analytic formulas are derived for the case of narrow band sensitivity configuration of the detector.