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COVID-19 is causing havoc to human health and the world economy right now. It is a single standard positive-sense RNA virus which is transferred by inhalation of a viral droplet. Its genome forms four structural proteins such as nucleocapsid protein, membrane protein, spike protein, and envelop protein. The capsid of coronavirus is a protein shell within which a positive strand of RNA is present which enables the virus to control the machinery of human cells. It has several variants, e.g., SARS, MERS, and now a new variant identified in 2019, which is a novel coronavirus that causes novel coronavirus disease (COVID-19). COVID-19 is a novel coronavirus disease that originally arose in Wuhan, China, and quickly spread around the world. Clinically, we identified the virus presence by a PCR-based test. Preventive measures and vaccination are the only treatment against coronavirus. Some of these include Remdesivir (GS-5734), Chloroquine, Hydroxychloroquine, and Theaflavin. A topological index (TI) is a mathematical function that assigns a numerical value to a (molecular) graph and predicts many physical, chemical, biological, thermodynamical, and structural features of that network. In this work, we will calculate a new topological index, namely, the first and second Gourava and Hyper-Gourava indices for the molecular graph of Remdesivir (GS-5734), Chloroquine, Hydroxychloroquine, and Theaflavin. We also plotted our computed results to examine how they were affected by the parameters involved. These findings could contribute in the development of new COVID-19 therapy options. [ABSTRACT FROM AUTHOR]