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.

Accelerating food safety and quality control: The use of antibody engineering techniques in the detec-tion of low-molecular weight food contaminants

The increased awareness and evolved consumer habits have set more demanding standards for the quality and safety control of food products. The production of foodstuffs which fulfill these standards can be hampered by different low-molecular weight contaminants. Such compounds can consist of, for example residues of antibiotics in animal use or mycotoxins. The extremely small size of the compounds has hindered the development of analytical methods suitable for routine use, and the methods currently in use require expensive instrumentation and qualified personnel to operate them. There is a need for new, cost-efficient and simple assay concepts which can be used for field testing and are capable of processing large sample quantities rapidly. Immunoassays have been considered as the golden standard for such rapid on-site screening methods. The introduction of directed antibody engineering and in vitro display technologies has facilitated the development of novel antibody based methods for the detection of low-molecular weight food contaminants. The primary aim of this study was to generate and engineer antibodies against low-molecular weight compounds found in various foodstuffs. The three antigen groups selected as targets of antibody development cause food safety and quality defects in wide range of products: 1) fluoroquinolones: a family of synthetic broad-spectrum antibacterial drugs used to treat wide range of human and animal infections, 2) deoxynivalenol: type B trichothecene mycotoxin, a widely recognized problem for crops and animal feeds globally, and 3) skatole, or 3-methyindole is one of the two compounds responsible for boar taint, found in the meat of monogastric animals. This study describes the generation and engineering of antibodies with versatile binding properties against low-molecular weight food contaminants, and the consecutive development of immunoassays for the detection of the respective compounds.