Unraveling a Nonlinear Coronavirus Model: An Evolutionary Approach to Dynamic Analysis

Abstract

The COVID-19 epidemic has underlined the vital need of thorough mathematical models to project disease trends and evaluate intervention strategies. Combining vaccination rates (v) and transmission characteristics (\u03b2), this study develops an improved SEIR (Susceptible-Exposed-Infected-Recovered) epidemic model to investigate the spread of COVID-19. By means of stability analysis, we find disease-free and endemic equilibrium points showing that more vaccination coverage significantly reduces the fundamental reproduction number (R₀), hence stabilizing the system. Using the Runge-Kutta method and a novel Evolutionary Padé-Approximation (EPA) approach, which combines Padé rational functions with Differential Evolution optimization to preserve accuracy while following model constraints (positivity, boundedness, and feasibility), numerical solutions are obtained. Even under high transmission conditions (β = 14), simulations show that improved vaccination speeds the decline of susceptible and infected populations while increasing recoveries, hence lowering R₀ below 1 at 50-100% vaccination rates. Comparative studies of the Runge-Kutta and EPA techniques show notable agreement, hence confirming EPA as a viable substitute for large-scale epidemiological modeling. Our results highlight the vital need of immunization in controlling COVID-19 and provide a computational tool for legislators to strengthen containment initiatives.