Evolutionary Invasion Analysis of Concurrent Multi-Strain Corona-Virus with Dynamic Virulence

Understanding the dynamics of COVID-19 requires models that go beyond classical assumptions. While various mathematical frameworks, including those based on evolutionary invasion analysis and multi-strain epidemic models, have the common limitation of treating virulence as a constant. In this study, we develop an advanced SIRD model that integrates time-dependent virulence to bridge the gap between evolutionary theory and epidemiological dynamics. We employ a finite difference method to compute virulence dynamically, using real-time data on daily infections and deaths to estimate mortality rates. This allows us to capture the evolving nature of virulence more realistically than traditional models. The basic reproduction number is derived and analyzed as a function of virulence, offering a nuanced perspective on transmission dynamics. Focusing on the United States data, we investigate the interplay and coexistence of multiple SARS-CoV-2 variants namely the original strain, Alpha, Delta, and Omicron. The model further quantifies the synergistic and antagonistic interactions among these strains. Their evolutionary fitness and invasion potential are assessed using invasion fitness functions and selection gradients, determining the intensity of invasion. Contour plots are used to visualize thresholds of the reproduction number, providing valuable insights into the evolutionary trajectories of viral strains. Our results emphasize the critical role of time-varying virulence and mutation-driven dynamics in shaping epidemic outcomes. The strains alpha, delta and resident strain interaction shows the synergism and omicron shows the antagonism behavior. This study offers a robust modeling framework that can inform future research and support evidence-based public health strategies.