The Covid-19 pandemic poses a significant threat to human health and life. Timely and accurate prediction of the epidemic’s trajectory is crucial for devising effective prevention and control strategies. Traditional infectious disease models may not capture the complexity of modern epidemics, especially when governments implement diverse policies. Drawing from China’s epidemic prevention strategies and Covid-19 transmission characteristics, this study introduces two distinct categories quarantined cases and asymptomatic cases to enhance the traditional SEIR model in depicting disease dynamics. To address the intricate nature of prevention and control efforts, the quarantined cases are further segmented into three subgroups: exposed quarantined, asymptomatic quarantined, and infected quarantined cases. Consequently, a novel SQEAIR model is proposed to model the dynamics of Covid-19. Evaluation metrics such as the Akaike information criterion (AIC) and Absolute Percentage Error (MAE) are employed to assess the efficacy and accuracy of both the newly proposed and traditional models. By fitting the models to the number of infected cases in Shanghai (March to May 2022) and Guangzhou (November 2022), it was observed that the SQEAIR model exhibited a lower AIC value compared to the SEIR model, indicating superior fitting accuracy for Covid-19 infections. Moreover, the high accuracy of the SQEAIR model enabled precise predictions of confirmed cases in Guangzhou. Leveraging the SQEAIR model, various parameters were tested to simulate the impact of different influencing factors, enabling the evaluation of defense strategies. These findings underscore the effectiveness of key epidemic control measures, such as quarantining exposed cases, in enhancing public health and promoting awareness of personal protection.