A SVEIR SARS-CoV-2 Omicron variant model is proposed to provide some insight to coordinate non-pharmaceutical interventions(NPIs) and vaccination. Mathematically, we define the basic reproduction number R0 and the effective reproduction number Re to measure the infection potential of Omicron variant and formulate a optimal disease control strategy. Our inversion results imply that the sick period of Omicron variant in the United States is longer than that of Delta variant in Indian; The decreasing of the infectious period of the infection with infectiousness implies that the risk of hospitalization is reduced; but the increasing period of the infection with non-infectiousness signifies that Omicron variant lengthens the period of nucleic acid test being negative; Optimistically, Omicron's death rate is only a quarter of Delta's. Moreover, we forecast that the cumulative cases will exceed 100 million in the United States on 28 February, 2022 and the daily confirmed cases will reach a peak on 2 February, 2022. The results of parameters sensitivity analysis imply that NPIs is helpful to reduce the number of confirmed cases. Especially, NPIs are indispensable even if all the people were vaccinated when the efficiency of vaccine is relatively low. By simulating the relation ships of the effective reproduction number Re , the vaccination rate and the efficacy of vaccine, we find that it is impossible to achieve the herd immunity without NPIs while the efficiency of vaccine is lower than 88.7%. Therefore, the herd immunity area is defined by the evolution of relationships between the vaccination rate and the efficacy of vaccine. Finally, we present that the disease-induced mortality rate demonstrates the periodic oscillation and an almost periodic function is deduced to match the curve. A discussion completes the paper.
AMS Subject Classification (2020): 34A34; 34D20; 92D30