The ability to comprehend the dynamics of viruses’ transmission and their evolution, even to a limited extent, can significantly enhance our capacity to predict and control the spread of infectious diseases. An example of such significance is COVID-19 caused by the severe acute respiratory syndrome Coronavirus 2 (SARS-CoV-2). In this dissertation, I am proposing computational models that present more precise and comprehensive approaches in viral outbreak investigations and epidemiology, providing invaluable insights into the transmission dynamics, and potential inter- ventions of infectious diseases by facilitating the timely detection of viral variants. The first model is a mathematical framework based on population dynamics for the calculation of a numerical measure of the fitness of SARS-CoV-2 subtypes. The second model I propose here is a transmissibility estimation method based on a Bayesian approach to calculate the most likely fitness landscape for SARS-CoV-2 using a generalized logistic sub-epidemic model. Using the proposed model I estimate the epistatic interaction networks of spike protein in SARS-CoV-2. Based on the community structure of these epistatic networks, I propose a computational framework that predicts emerging haplotypes of SARS-CoV-2 with altered transmissibility. The last method proposed in this dissertation is a maximum likelihood framework that integrates phylogenetic and random graph models to accurately infer transmission networks without requiring case-specific data.