A mathematical model for simulating the transmission dynamics of COVID-19 using the Caputo–Fabrizio fractional-order derivative with nonsingular kernel

The emergence of the new coronavirus variant from the coronaviridae family has become a global concern, and all nations, including Bangladesh, are battling to contain the spread of the disease. In this article, we discuss a COVID-19 vaccination model with the Caputo–Fabrizio (CF) fractional order derivative approach to reveal the complicated action in Bangladesh. We determine the existence and uniqueness properties of the outcomes acquired from our proposed model subjected to the Picard–Lindelöf theorem. We perform the stability analysis by using the fixed-point theorem. We utilize Laplace Transform to evaluate the approximate solution of the model. In the numerical simulation, we consider a new approach called the four-step Adams-Bashforth Predictor–Corrector iteration scheme, which simulates that the fractional order provides more precise results. Finally, several numerical results are displayed with the different numbers of the order of the system. We depict the influence of vaccination in the coronavirus model with different parameter values. By analyzing the transmission dynamics of the virus, we bring to light the importance of several doses of vaccination to prevent disease transmission and contagions. We also conducted the sensitivity analysis for the model parameters to evaluate the impact of those parameters on disease outbreaks. The numerical results demonstrate significant information in the Caputo–Fabrizio fractional derivative concept and provide important insights into predicting disease transmission and control policies.