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Antiviral medications, such as Arbidol, Chloroquine, Hydroxy-Chloroquine, Lopinavir, Remdesivir, Ritonavir, Thalidomide and Theaflavin, are often used to treat COVID-19. In this paper, we define Diameter Eccentricity Based vertex degree and employ it to introduce a new polynomial called $ D\\varepsilon- $ Polynomial. Using the newly introduced polynomial, we derive new topological indices, namely, diameter eccentricity based and hyper diameter eccentricity based indices. In order to check the efficacy of our indices, we derive the $ D\\varepsilon- $ polynomials for the eight COVID-19 drugs mentioned above. Using these polynomials, we compute our proposed topological descriptors for the eight COVID-19 drugs. We perform quantitative structure-property relationship (QSPR) analysis by identifying the best fit curvilinear\/multilinear regression models based on our topological descriptors for 8 physico- chemical properties of the COVID-19 drugs. We also perform quantitative structure-activity relationship (QSAR) analysis by identifying the best fit multilinear regression model for predicting the $ IC_{50} $ values for the eight COVID-19 drugs. Our findings and models may be useful in the development of new COVID-19 medication.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/mbe.2023769","type":"journal-article","created":{"date-parts":[[2023,9,5]],"date-time":"2023-09-05T10:19:15Z","timestamp":1693909155000},"page":"17272-17295","source":"Crossref","is-referenced-by-count":8,"title":["QSPR\/QSAR analysis of some eccentricity based topological descriptors of antiviral drugs used in COVID-19 treatment via $ \\mathscr{D}\\varepsilon $- polynomials"],"prefix":"10.3934","volume":"20","author":[{"given":"Deepalakshmi","family":"Sarkarai","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kalyani","family":"Desikan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2321","reference":[{"key":"key-10.3934\/mbe.2023769-1","doi-asserted-by":"publisher","unstructured":"M. Ahmad, D. Afzal, W. Nazeer, S. 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