We develop and analyze a ten-compartment nonlinear ODE model to investigate COVID-19 transmission dynamics in India’s first wave, explicitly incorporating environmental contamination, media-driven awareness, face-mask usage, quarantine, treatment saturation, and viral decay. Through dynamical systems theory, we establish positivity, boundedness, and derive the control reproduction number \(R_c\) via the next-generation matrix. Local stability of the disease-free equilibrium is shown for \(R_c<1\) , while global stability holds when treatment saturation is absent ( \(b=0\) ). Importantly, inclusion of a saturated treatment response ( \(b\ne 0\) ) induces a backward bifurcation at \(R_c=1\) , indicating that disease elimination may fail even if \(R_c<1\) . Model parameters are estimated by fitting to reported case data (March 2020–January 2021), and sensitivity analyses (normalized forward indices and PRCC) identify key drivers of transmission and prevalence. Finally, we formulate an optimal control problem with five time-dependent interventions, demonstrating that a coordinated strategy-combining mask mandates, media campaigns, quarantine, treatment scale-up, and disinfection-most effectively suppresses infections and prevents backward bifurcation traps. Our results offer actionable insights for designing multilayered public health policies to eliminate COVID-19.
