In Wuhan city of China, an episode of novel coronavirus (COVID-19) happened. during late December and it has quickly spread to all places in the world. Until May 29, 2020, cases were high in the USA with 1.7 Million, Russia with approximately 387 thousand, the UK with 271 thousand confirmed cases. Everybody on the planet is anxious to know when the coronavirus pandemic will end. In this scourge, most nations force extreme medication measures to contain the spread of COVID-19. Modeling has been utilized broadly by every national government and the World Health Organization in choosing the best procedures to seek after in relieving the impacts of COVID-19. Many epidemiological models are studied to understand the spread of the illness and its prediction to find maximum capacity for human-to-human transmission so that control techniques can be adopted. Also, arrangements for the medical facilities required such as hospital beds and medical supplies can be made in advance. Many models are used to anticipate the results keeping in view the present scenario. There is an urgent need to study the various models and their impacts. In this study, we present a systematic literature review on epidemiological models for the outbreak of novel coronavirus in India. The epidemiological dynamics of COVID-19 is also studied. Here, In addition, an attempt to take out the results from the exploration and comparing it with the real data. The study helps to choose the models that are progressive and dependable to predict and give legitimate methods for various strategies.