The genetic structure of an intra-host viral population has an effect on many clinically important phenotypic traits such as escape from vaccine induced immunity, virulence, and response to antiviral therapies. Next-generation sequencing provides read-coverage sufficient for genomic reconstruction of a heterogeneous, yet highly similar, viral population; and more specifically, for the detection of rare variants. Admittedly, while depth is less of an issue for modern sequencers, the short length of generated reads complicates viral population assembly. This task is worsened by the presence of both random and systematic sequencing errors in huge amounts of data. In this dissertation I present completed work for reconstructing a viral population given next-generation sequencing data. Several algorithms are described for solving this problem under the error-free amplicon (or sliding-window) model. In order for these methods to handle actual real-world data, an error-correction method is proposed. A formal derivation of its likelihood model along with optimization steps for an EM algorithm are presented. Although these methods perform well, they cannot take into account paired-end sequencing data. In order to address this, a new method is detailed that works under the error-free paired-end case along with maximum a-posteriori estimation of the model parameters.

This thesis is devoted to designing and applying advanced algorithmical and statistical tools for analysis of NGS data related to cancer and infection diseases. NGS data under investigation are obtained either from host samples or viral variants. Recently, random peptide phage display libraries (RPPDL) were applied to studies of host's antibody response to different diseases. We study human antibody response to breast cancer and mouse antibody response to Lyme disease by sequencing of the whole antibody repertoire profiles which are represented by RPPDL. Alternatively, instead of sequencing immune response NGS can be applied directly to a viral population within an infected host. Specifically, we analyze the following RNA viruses: the human immunodeficiency virus (HIV) and the infectious bronchitis virus (IBV). Sequencing of RNA viruses is challenging because there are many variants inside population due to high mutation rate. Our results show that NGS helps to understand RNA viruses and explore their interaction with infected hosts. NGS also helps to analyze immune response to different diseases, trace changing of immune response at different disease stages.