The COVID-19 pandemic has posed unprecedented challenges to global public health, sparking intense investigation into its transmission dynamics, control strategies, and viral evolution. This work explores the epidemiological, genomic, and evolutionary aspects of SARS-CoV-2 and Hepatitis C Virus (HCV), shedding light on the role of non-pharmaceutical interventions (NPIs), viral spread, and intra-host viral diversity. Phylogenetic and phylodynamic analyses were used to study the early course of COVID-19 in Ukraine. Results show that even short delays in implementing NPIs could have significantly increased case numbers and overwhelmed healthcare systems. Genomic analysis revealed multiple independent introductions of SARS-CoV-2 into the country, with evidence of sustained local transmission. Estimates of the basic reproduction number from both case data and genomic sequences support these conclusions and suggest that travel restrictions had limited impact on virus importation. In Belarus, where NPIs were minimal, genomic surveillance and phylodynamic modeling were employed to understand SARS-CoV-2 dynamics. The cumulative number of infections by mid-2020 was likely underreported by a factor of approximately four. At least 18 separate introductions of the virus were detected, followed by considerable regional transmission. Although limited interventions modestly reduced the effective reproduction number, its trajectory remained comparable to neighboring regions with stricter measures, highlighting the influence of sociodemographic and regional factors in shaping epidemic outcomes. To investigate intra-host viral evolution, epistatic interactions among single-nucleotide variants (SNVs) in Hepatitis C Virus populations were analyzed. A novel metric, epistatic density, was introduced to quantify co-occurrence of positively linked SNV pairs within viral genomes. Analysis of populations from acute and chronic HCV infections revealed higher and more structured epistatic density in chronic cases, indicating differential selective pressures over the course of infection. Epistatic density features also enabled successful classification of viral populations by infection stage.