In response to the spread of the novel coronavirus pneumonia (COVID-19) in India, this paper proposes to establish a SIR infectious disease dynamic model that determines the unknown parameters of the model by setting the objective function and seeking the optimal solution. First, the parameter range is fitted by linear regression, the objective function is set as the constraint condition, and the Runge-Kutta method is combined with the Matlab software to determine the optimal solution of the parameter value, and the SIR model is fitted and predicted. It is found that the inflection point of the epidemic in India will appear around May 8, 2021, and the number of new daily and cumulative new cases in the future is derived based on the forecast data. Although new cases will continue to appear in the next 100 days, the current epidemic situation has already subsided. Secondly, considering the influence of the Indian variant virus B. 1. 617 and the current vaccination situation, a SIR prediction model with vaccine influencing factors was established. Based on the vaccination sensitivity analysis, it is simulated that the vaccination rate in India needs to reach about 75%, and considering the effective protection rate, the vaccination rate needs to be as high as 95%, so that the herd immunity barrier can be established. Finally, the vaccination rate was verified by the basic infection number, and the corresponding countermeasures were analyzed for the impact of COVID-19.