A vaccination model for COVID-19 with asymptomatic transmission, waning immunity, and outbreak calibration.

The COVID-19 pandemic has posed unprecedented challenges to global public health, revealing critical gaps in our understanding of transmission dynamics, particularly the roles of asymptomatic spread and waning immunity. To address these gaps, we develop a mathematical model of COVID-19 transmission that incorporates asymptomatic and symptomatic pathways, vaccination dynamics, and the waning of both vaccine-induced and naturally acquired immunity. The basic reproduction number R 0 is derived and decomposed into three transmission pathways: direct asymptomatic transmission, direct symptomatic transmission, and asymptomatic-to-symptomatic progression. This decomposition enables quantification of the contribution of asymptomatic spread to disease persistence. Numerical simulations show that vaccination coverage and vaccine durability jointly shape long-term epidemic burden, while natural immunity waning is critical for endemic persistence. Calibration of the model to an outbreak in Nanjing, China, yields excellent fit (R 2 = 0.9617) and reveals that asymptomatic transmission accounts for approximately 53.7% of the modeled transmission potential. The integrated framework provides both mathematical rigor for analyzing disease dynamics and practical insights for evidence-based pandemic response, highlighting the need for adaptive control strategies that address asymptomatic transmission and waning immunity.