Abstract
This manuscript is devoted to investigating the effectiveness of vaccination in the current outbreak of COVID-19 by modeling a three-compartments model. The proposed model includes susceptible, infected, and vaccinated classes (we abbreviate as SIV). In this regard, some graphical presentations are provided under the said noise terms. Furthermore, the model is treated under piecewise equations of nonsingular kernel-type derivative of ABC. We derive some fundamental results about the feasibility and positivity of the solution in the sense of nonsingular-type derivative by using Laplace transform. Also, we compute the strengthen number by the matrix method. Moreover, we simulate the model by using a powerful numerical algorithm by taking some real data for initial values of vaccinated and infected classes. We investigate the proposed model under stochastic noise by using stochastic differential equations (SDEs).