Stability and sensitivity analysis of a COVID-19 model with immunity development and case confirmation delay

This study presents a mathematical model to analyse how delays in case confirmation and immunity development influence COVID-19 transmission and control. A delay function captures diagnostic lags, directly impacting the basic reproduction number ([Formula: see text]) and the success of interventions. The model identifies disease-free and endemic equilibria, with stability linked to [Formula: see text] and critical delay thresholds. Sensitivity analysis reveals that increasing delays significantly raise [Formula: see text], reducing the effectiveness of isolation and vaccination efforts. Numerical simulations confirm that early case detection and timely immunity development are important for reducing transmission. This model provides essential insights into how minimizing delays can lower [Formula: see text], guiding more effective public health strategies for COVID-19 containment.