This study proposes and analyzes a mathematical model for the transmission dynamics of COVID-19, explicitly accounting for the ability of the immune system in some individuals to eliminate the virus before they become infectious. A compartmental Susceptible–Exposed–Asymptomatic–Symptomatic–Hospitalized–Recovered (SEAIHR) model is formulated using both classical integer-order derivatives and Caputo fractional-order derivatives. The model is first examined by establishing the positivity and boundedness of solutions, followed by the computation of the basic reproduction number R0. The existence of equilibrium points is proven, and the asymptotic stability of the disease-free equilibrium is analyzed when R0 < 1. Epidemiological data from Cameroon are used to estimate model parameters and calibrate the system. Sensitivity analysis identifies the most influential parameters governing disease transmission. Numerical results indicate that R0 ≈ 1.6483, suggesting that COVID-19 remains endemic despite declining mortality. Simulations further show that enhanced immune responses may contribute to the relatively low morbidity observed in sub-Saharan Africa.