Bayesian analysis of SEIR epidemic models

This thesis concerns the analysis of epidemic models. We adopt the Bayesian paradigm and develop suitable Markov Chain Monte Carlo (MCMC) algorithms. This is done by considering an Ebola outbreak in the Democratic Republic of Congo, former Zaïre, 1995 as a case of SEIR epidemic models. We model the Ebola epidemic deterministically using ODEs and stochastically through SDEs to take into account a possible bias in each compartment. Since the model has unknown parameters, we use different methods to estimate them such as least squares, maximum likelihood and MCMC. The motivation behind choosing MCMC over other existing methods in this thesis is that it has the ability to tackle complicated nonlinear problems with large number of parameters. First, in a deterministic Ebola model, we compute the likelihood function by sum of square of residuals method and estimate parameters using the LSQ and MCMC methods. We sample parameters and then use them to calculate the basic reproduction number and to study the disease-free equilibrium. From the sampled chain from the posterior, we test the convergence diagnostic and confirm the viability of the model. The results show that the Ebola model fits the observed onset data with high precision, and all the unknown model parameters are well identified. Second, we convert the ODE model into a SDE Ebola model. We compute the likelihood function using extended Kalman filter (EKF) and estimate parameters again. The motivation of using the SDE formulation here is to consider the impact of modelling errors. Moreover, the EKF approach allows us to formulate a filtered likelihood for the parameters of such a stochastic model. We use the MCMC procedure to attain the posterior distributions of the parameters of the SDE Ebola model drift and diffusion parts. In this thesis, we analyse two cases: (1) the model error covariance matrix of the dynamic noise is close to zero , i.e. only small stochasticity added into the model. The results are then similar to the ones got from deterministic Ebola model, even if methods of computing the likelihood function are different (2) the model error covariance matrix is different from zero, i.e. a considerable stochasticity is introduced into the Ebola model. This accounts for the situation where we would know that the model is not exact. As a results, we obtain parameter posteriors with larger variances. Consequently, the model predictions then show larger uncertainties, in accordance with the assumption of an incomplete model.

Méthode efficace d'assignation de tissus humains par tomodensitométrie à double énergie

Pour analyser les images en tomodensitométrie, une méthode stœchiométrique est gé- néralement utilisée. Une courbe relie les unités Hounsfield d’une image à la densité électronique du milieu. La tomodensitométrie à double énergie permet d’obtenir des informations supplémentaires sur ces images. Une méthode stœchiométrique a été dé- veloppée pour permettre de déterminer les valeurs de densité électronique et de numéro atomique effectif à partir d’une paire d’images d’un tomodensitomètre à double énergie. Le but de cette recherche est de développer une nouvelle méthode d’identification de tissus en utilisant ces paramètres extraits en tomodensitométrie à double énergie. Cette nouvelle méthode est comparée avec la méthode standard de tomodensitométrie à simple énergie. Par ailleurs, l’impact dosimétrique de bien identifier un tissu est déterminé. Des simulations Monte Carlo permettent d’utiliser des fantômes numériques dont tous les paramètres sont connus. Les différents fantômes utilisés permettent d’étalonner les méthodes stœchiométriques, de comparer la polyvalence et la robustesse des méthodes d’identification de tissus double énergie et simple énergie, ainsi que de comparer les distributions de dose dans des fantômes uniformes de mêmes densités, mais de compo- sitions différentes. La méthode utilisant la tomodensitométrie à double énergie fournit des valeurs de densi- tés électroniques plus exactes, quelles que soient les conditions étudiées. Cette méthode s’avère également plus robuste aux variations de densité des tissus. L’impact dosimé- trique d’une bonne identification de tissus devient important pour des traitements aux énergies plus faibles, donc aux énergies d’imagerie et de curiethérapie.

Radiopaque materials from natural polymers: Special emphasis on chitosan and natural rubber

The present work is to impart radiopacity in various natural polymers like chitosan, natural rubber and derivatives of chitosan and to characterize it. This thesis collated the radiopaque properties of these radiopaque polymers and various technological applications in the medical field. The applications of radiopaque polymers leads to an exploitation of radiopaque properties like X-ray visibility, optical density, effective atomic number, attenuation coefficient of biopolymers like chitosan, chitosan formate, chitosan acetate, carboxy methyl chitosan and natural rubber. The radiopaqe properties of these materials highly depend upon the size, shape, amount of radiopacifier and crystallinity of the radiopaque material. Radiopaque chitosan microspheres were prepared by cross linking with glutaraldehyde followed by the encapsulation of barium sulpahte. The effect of different emulsion systems on the morphology of chitosan microspheres were studied. The study concentrates radiopaque natural rubber for shielding applications. It reveals that to improve the particle size, morphology and crystalline phase of the zinc oxide particles, a novel method for the preparation of zinc oxide is adopted. A detailed radiopacity study was done in natural rubber containing 100phr precipitated zinc oxide prepared from different zinc salts. One of the significant findings of this investigation is that NR vulcanizates containing precipitated zinc oxide (from zinc acetate) shows higher attenuation coefficient. These interesting findings reveal the applications of these natural radiopaque systems in various fields like surgical tools, medical tubings, catheters, radiation shielding,etc.

A mathematical model for the dynamics of Banana Xanthomonas Wilt with vertical transmission and inflorescence infection

A mathematical model for Banana Xanthomonas Wilt (BXW) spread by insect is presented. The model incorporates inflorescence infection and vertical transmission from the mother corm to attached suckers, but not tool-based transmission by humans. Expressions for the basic reproduction number R0 are obtained and it is verified that disease persists, at a unique endemic level, when R0 > 1. From sensitivity analysis, inflorescence infection rate and roguing rate were the parameters with most influence on disease persistence and equilibrium level. Vertical transmission parameters had less effect on persistence threshold values. Parameters were approximately estimated from field data. The model indicates that single stem removal is a feasible approach to eradication if spread is mainly via inflorescence infection. This requires continuous surveillance and debudding such that a 50% reduction in inflorescence infection and 2–3 weeks interval of surveillance would eventually lead to full recovery of banana plantations and hence improved production.

Estrutura genética de populações de Trichilia pallida Swartz (Meliaceae) por marcadores RAPD

Trichilia pallida Swartz is an Atlantic Forest shady climax tree of Meliaceae family that presents insecticide properties against chewing insects like as some family trees, making it interesting for forestry uses. Forty plants of Oito Pontas Farm population were collected in Bofete County, Santa Genebra Ecological Station in Campinas County, and Caetetus Ecological Station in Gélia County, all in the Sao Paulo State, Brazil. Leaf DNA analysis was used by RAPD method, that showed 10 highly polymorphic primers, with 72 dominant markers, used to estimate genetic diversity within and among populations. The polymorphism within populations varied from 90.3 to 97.2%, and the effective allele number varied from 1.46 ± 0.33 to 1.57 ± 0.33, while the average of genetic differentiation of populations varied from 0.27 ± 0.18 to 0, 33 ± 0.15. The gene diversity in the total population (H T) was 0.334 ± 0.02, while the average gene diversity within populations (H s) was 0.292 ± 0.017, and the coefficient of gene differentiation (G ST) was 0.125, Bofete and Campinas populations had the smallest Nei's genetic distance (0.049) and the distances of both with Gália were 0.117 and 0.107, respectively.

Biodiversity Can Help Prevent Malaria Outbreaks in Tropical Forests

Background: Plasmodium vivax is a widely distributed, neglected parasite that can cause malaria and death in tropical areas. It is associated with an estimated 80-300 million cases of malaria worldwide. Brazilian tropical rain forests encompass host- and vector-rich communities, in which two hypothetical mechanisms could play a role in the dynamics of malaria transmission. The first mechanism is the dilution effect caused by presence of wild warm-blooded animals, which can act as dead-end hosts to Plasmodium parasites. The second is diffuse mosquito vector competition, in which vector and non-vector mosquito species compete for blood feeding upon a defensive host. Considering that the World Health Organization Malaria Eradication Research Agenda calls for novel strategies to eliminate malaria transmission locally, we used mathematical modeling to assess those two mechanisms in a pristine tropical rain forest, where the primary vector is present but malaria is absent. Methodology/Principal Findings: The Ross-Macdonald model and a biodiversity-oriented model were parameterized using newly collected data and data from the literature. The basic reproduction number (R0) estimated employing Ross-Macdonald model indicated that malaria cases occur in the study location. However, no malaria cases have been reported since 1980. In contrast, the biodiversity-oriented model corroborated the absence of malaria transmission. In addition, the diffuse competition mechanism was negatively correlated with the risk of malaria transmission, which suggests a protective effect provided by the forest ecosystem. There is a non-linear, unimodal correlation between the mechanism of dead-end transmission of parasites and the risk of malaria transmission, suggesting a protective effect only under certain circumstances (e.g., a high abundance of wild warm-blooded animals). Conclusions/Significance: To achieve biological conservation and to eliminate Plasmodium parasites in human populations, the World Health Organization Malaria Eradication Research Agenda should take biodiversity issues into consideration. © 2013 Laporta et al.

Uma abordagem probabilística do número de reprodução básica em modelos epidemiológicos com aplicação na ferrugem do eucalipto

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Diversidade genética em coleções amazônicas de germoplasma de cupuaçuzeiro [Theobroma grandiflorum (Willd. ex Spreng.) Schum.]

This study aimed to evaluate the genetic diversity and relatedness of 24 accessions of Theobroma grandiflorum, originating from three units of Embrapa, aiming their use as parents in hybridization specie programs. The genetic markers used were heterologous microsatellite loci developed for cocoa. In the population studied 45 alleles were found. The effective average number of alleles per locus (2.33) was less than the average number of alleles per locus (3.21), indicating that many alleles have low frequency. The observed heterozygosity at polymorphic loci ranged from 0.33 to 1.00 with a mean of 0.54 and expected heterozygosity ranged from 0.48 to 0.76 with a mean of 0.54. The fixation index medium between loci (0.003) was not significantly different from zero. The estimate of relatedness between pairs of individuals indicates that some may be relatives, including half-brothers and clones. The results suggest that the accesses of T. grandiflorum analyzed contain a moderate level of genetic diversity and absence of inbreeding and therefore great potential for use in breeding programs.

Landscape Diversity Influences Dispersal and Establishment of Pest with Complex Nutritional Ecology

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Compton scattering spectrum as a source of information of normal and neoplastic breast tissues' composition

In this work we measured X-ray scatter spectra from normal and neoplastic breast tissues using photon energy of 17.44 key and a scattering angle of 90 degrees, in order to study the shape (FWHM) of the Compton peaks. The obtained results for FWHM were discussed in terms of composition and histological characteristics of each tissue type. The statistical analysis shows that the distribution of FWHM of normal adipose breast tissue clearly differs from all other investigated tissues. Comparison between experimental values of FWHM and effective atomic number revealed a strong correlation between them, showing that the FWHM values can be used to provide information about elemental composition of the tissues. (C) 2012 Elsevier Ltd. All rights reserved.

Sviluppo di un tomografo multi-energy per lo studio pre-clinico di nuove metodiche diagnostiche finalizzate al riconoscimento precoce della patologia tumorale

A new multi-energy CT for small animals is being developed at the Physics Department of the University of Bologna, Italy. The system makes use of a set of quasi-monochromatic X-ray beams, with energy tunable in a range from 26 KeV to 72 KeV. These beams are produced by Bragg diffraction on a Highly Oriented Pyrolytic Graphite crystal. With quasi-monochromatic sources it is possible to perform multi-energy investigation in a more effective way, as compared with conventional X-ray tubes. Multi-energy techniques allow extracting physical information from the materials, such as effective atomic number, mass-thickness, density, that can be used to distinguish and quantitatively characterize the irradiated tissues. The aim of the system is the investigation and the development of new pre-clinic methods for the early detection of the tumors in small animals. An innovative technique, the Triple-Energy Radiography with Contrast Medium (TER), has been successfully implemented on our system. TER consist in combining a set of three quasi-monochromatic images of an object, in order to obtain a corresponding set of three single-tissue images, which are the mass-thickness map of three reference materials. TER can be applied to the quantitative mass-thickness-map reconstruction of a contrast medium, because it is able to remove completely the signal due to other tissues (i.e. the structural background noise). The technique is very sensitive to the contrast medium and is insensitive to the superposition of different materials. The method is a good candidate to the early detection of the tumor angiogenesis in mice. In this work we describe the tomographic system, with a particular focus on the quasi-monochromatic source. Moreover the TER method is presented with some preliminary results about small animal imaging.

Epidemiologia delle strongilosi dell'asino: quali applicazioni per il controllo delle infezioni da elminti?

Strongylosis in equids, despite being very common, have never been studied from a strictly ecological point of view. Mathematical models are important ecological tools used to study the temporal dynamics of parasite populations, and are useful to study the effect of different biological parameters, as well as to analyse the outcome produced by perturbations such as anthelmintic treatments. This work describes the study of the temporal dynamics of strongyles infection in an organic donkey population, performed using coprological quantitative analysis and donkeys’ age as a proxy of the time of infection. Force of infection was then estimated for Strongylus vulgaris and small strongyles and the results used as the basis for the development of mathematical models. In particular, the comparison of models output and field data made it possible to estimate the transmission coefficient  and to consequently calculate the basic reproduction number R0 and the threshold host density. Small strongyles model includes hypobiosis and, more interestingly as never found in literature, a density-dependent development rate of hypobiotic larvae in adult parasites in order to simulate a negative feedback between larvae emergence from hypobiosis and adult parasite abundance. Simulations of pharmacological and environmental treatments showed that parasite eradication was possible for S. vulgaris only, while small strongyles, due to hypobiosis and density-dependent development rate of their hypobiotic larvae, are very difficult to control and impossible to eradicate. In addition, density-dependence in larval development has been demonstrated to act as a key factor in improving parasite population survival and abundance even in absence of human intervention.

DUAL ENERGY COMPUTED TOMOGRAPHY FOR PROTON THERAPY TREATMENT PLANNING

Proton radiation therapy is gaining popularity because of the unique characteristics of its dose distribution, e.g., high dose-gradient at the distal end of the percentage-depth-dose curve (known as the Bragg peak). The high dose-gradient offers the possibility of delivering high dose to the target while still sparing critical organs distal to the target. However, the high dose-gradient is a double-edged sword: a small shift of the highly conformal high-dose area can cause the target to be substantially under-dosed or the critical organs to be substantially over-dosed. Because of that, large margins are required in treatment planning to ensure adequate dose coverage of the target, which prevents us from realizing the full potential of proton beams. Therefore, it is critical to reduce uncertainties in the proton radiation therapy. One major uncertainty in a proton treatment is the range uncertainty related to the estimation of proton stopping power ratio (SPR) distribution inside a patient. The SPR distribution inside a patient is required to account for tissue heterogeneities when calculating dose distribution inside the patient. In current clinical practice, the SPR distribution inside a patient is estimated from the patient’s treatment planning computed tomography (CT) images based on the CT number-to-SPR calibration curve. The SPR derived from a single CT number carries large uncertainties in the presence of human tissue composition variations, which is the major drawback of the current SPR estimation method. We propose to solve this problem by using dual energy CT (DECT) and hypothesize that the range uncertainty can be reduced by a factor of two from currently used value of 3.5%. A MATLAB program was developed to calculate the electron density ratio (EDR) and effective atomic number (EAN) from two CT measurements of the same object. An empirical relationship was discovered between mean excitation energies and EANs existing in human body tissues. With the MATLAB program and the empirical relationship, a DECT-based method was successfully developed to derive SPRs for human body tissues (the DECT method). The DECT method is more robust against the uncertainties in human tissues compositions than the current single-CT-based method, because the DECT method incorporated both density and elemental composition information in the SPR estimation. Furthermore, we studied practical limitations of the DECT method. We found that the accuracy of the DECT method using conventional kV-kV x-ray pair is susceptible to CT number variations, which compromises the theoretical advantage of the DECT method. Our solution to this problem is to use a different x-ray pair for the DECT. The accuracy of the DECT method using different combinations of x-ray energies, i.e., the kV-kV, kV-MV and MV-MV pair, was compared using the measured imaging uncertainties for each case. The kV-MV DECT was found to be the most robust against CT number variations. In addition, we studied how uncertainties propagate through the DECT calculation, and found general principles of selecting x-ray pairs for the DECT method to minimize its sensitivity to CT number variations. The uncertainties in SPRs estimated using the kV-MV DECT were analyzed further and compared to those using the stoichiometric method. The uncertainties in SPR estimation can be divided into five categories according to their origins: the inherent uncertainty, the DECT modeling uncertainty, the CT imaging uncertainty, the uncertainty in the mean excitation energy, and SPR variation with proton energy. Additionally, human body tissues were divided into three tissue groups – low density (lung) tissues, soft tissues and bone tissues. The uncertainties were estimated separately because their uncertainties were different under each condition. An estimate of the composite range uncertainty (2s) was determined for three tumor sites – prostate, lung, and head-and-neck, by combining the uncertainty estimates of all three tissue groups, weighted by their proportions along typical beam path for each treatment site. In conclusion, the DECT method holds theoretical advantages in estimating SPRs for human tissues over the current single-CT-based method. Using existing imaging techniques, the kV-MV DECT approach was capable of reducing the range uncertainty from the currently used value of 3.5% to 1.9%-2.3%, but it is short to reach our original goal of reducing the range uncertainty by a factor of two. The dominant source of uncertainties in the kV-MV DECT was the uncertainties in CT imaging, especially in MV CT imaging. Further reduction in beam hardening effect, the impact of scatter, out-of-field object etc. would reduce the Hounsfeld Unit variations in CT imaging. The kV-MV DECT still has the potential to reduce the range uncertainty further.

Ebola virus disease outbreak in Nigeria: Transmission dynamics and rapid control.

International air travel has already spread Ebola virus disease (EVD) to major cities as part of the unprecedented epidemic that started in Guinea in December 2013. An infected airline passenger arrived in Nigeria on July 20, 2014 and caused an outbreak in Lagos and then Port Harcourt. After a total of 20 reported cases, including 8 deaths, Nigeria was declared EVD free on October 20, 2014. We quantified the impact of early control measures in preventing further spread of EVD in Nigeria and calculated the risk that a single undetected case will cause a new outbreak. We fitted an EVD transmission model to data from the outbreak in Nigeria and estimated the reproduction number of the index case at 9.0 (95% confidence interval [CI]: 5.2-15.6). We also found that the net reproduction number fell below unity 15 days (95% CI: 11-21 days) after the arrival of the index case. Hence, our study illustrates the time window for successful containment of EVD outbreaks caused by infected air travelers.

Dynamics of a Tularemia Outbreak in a Closely Monitored Free-Roaming Population of Wild House Mice.

Infectious disease outbreaks can be devastating because of their sudden occurrence, as well as the complexity of monitoring and controlling them. Outbreaks in wildlife are even more challenging to observe and describe, especially when small animals or secretive species are involved. Modeling such infectious disease events is relevant to investigating their dynamics and is critical for decision makers to accomplish outbreak management. Tularemia, caused by the bacterium Francisella tularensis, is a potentially lethal zoonosis. Of the few animal outbreaks that have been reported in the literature, only those affecting zoo animals have been closely monitored. Here, we report the first estimation of the basic reproduction number R0 of an outbreak in wildlife caused by F. tularensis using quantitative modeling based on a susceptible-infected-recovered framework. We applied that model to data collected during an extensive investigation of an outbreak of tularemia caused by F. tularensis subsp. holarctica (also designated as type B) in a closely monitored, free-roaming house mouse (Mus musculus domesticus) population in Switzerland. Based on our model and assumptions, the best estimated basic reproduction number R0 of the current outbreak is 1.33. Our results suggest that tularemia can cause severe outbreaks in small rodents. We also concluded that the outbreak self-exhausted in approximately three months without administrating antibiotics.