Abstract
<abstract><p>The goal of this manuscript is to use a mathematical model with four compartments to examine the positive effects of rotavirus vaccinations. Susceptible, vaccinated, infected, and recovered (SVIR) classes are included in the suggested model. Some qualitative conclusions are established for the complicated pediatric disease epidemic model of rotavirus, which travels through a population at an inconsistent rate. The model has been fitted with piecewise equations of non-singular kernel-type derivatives in the modified Atangana-Balaneu-Caputo $ (mABC) $ sense. Using the Laplace transform and the notion of non-singular-type derivatives, we prove several basic conclusions regarding the solution's feasibility and positivity. We have used the matrix approach to compute the reproductive number further. Also, the sensitivity of the model has been computed. Additionally, we have used an efficient numerical approach to simulate the model by using some numerical values for the nomenclature of the model. Additionally, using the numerical approach, various graphical illustrations are given.</p></abstract>
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