Impact of vaccine measures on the transmission dynamics of COVID-19

In many nations, efforts to prevent and control COVID-19 have been significantly impeded by the SARS-CoV-2 virus ongoing mutation. The Omicron strain, a more recent and prevalent strain, has had more significant detrimental effects in countries worldwide. To investigate the impact of the Omicron BA.2 strain on vaccine efficacy, we proposed a model with vaccination and immunological decline in this research. Then, we fitted our model based on the number of daily new instances reported by the government in Jilin and Shanghai, China. We estimated the effective reproduction number R(e) = 4.71 for the Jilin and R(e) = 3.32 for Shanghai. Additionally, we do sensitivity analysis to identify the critical factors affecting the effective reproduction number R(e). It was found that vaccination rate, effectiveness rate, and declining rate had a significant effect on R(e). Further, we investigate the relevant parameter thresholds that make R(e) lower than unity. Finally, rich numerical experiments were then carried out. We observed that even when vaccine efficiency was not high, increasing vaccination rates had a significant effect on early disease transmission, that limiting social distance was the most economical and rational measure to control the spread of disease, and that for a short period, reducing immune decline was not significant in curbing disease transmission.