Understanding the dynamics of the COVID-19 pandemic is crucial for improved control and social distancing strategies. To that effect, we have employed the susceptible-exposed-infectious-recovered model, refined by contact tracing and hospitalization data from Indian provinces Kerala, Delhi, Maharashtra, and West Bengal, as well as from overall India. We have performed a sensitivity analysis to identify the most crucial input parameters, and we have calibrated the model to describe the data as best as possible. Short-term predictions reveal an increasing and worrying trend of COVID-19 cases for all four provinces and India as a whole, while long-term predictions also reveal the possibility of oscillatory dynamics. Our research thus leaves the option open that COVID-19 might become a seasonal occurrence. We also simulate and discuss the impact of media on the dynamics of the COVID-19 pandemic.