A Fractional Sars-Cov-2 Model With Atangana–Baleanu Derivative: Application To Fourth Wave

A dynamical model of SARS-CoV-2 in fractional derivative using the cases of coronavirus of the fourth wave is presented. We construct basically the model in an integer case, and later it is extended to a fractional-order system by applying the Atangana–Baleanu operator definition. We give some background definitions and results for the fractional-order model. We present for the disease-free case that the model is locally asymptotically stable when ℛ0 < 1. The global dynamics of the fractional model are given when ℛ0 ≤ 1 for the disease-free case. The model is further extended to fractional stochastic piecewise equations in the Atangana–Baleanu case. The reported cases from the fourth wave in Pakistan starting from July 1 up to November 16, 2021 are considered for the estimation of the parameters. We fitted our model to the suggested data and obtained the numerical value of the basic reproduction number ℛ0 ≈ 0.9775 for fractional order. We give the data fitting to both the fractional and piecewise stochastic differential equations, and show them both as having a good fitting to the data. We use further the numerical values of the model parameters and present its numerical results graphically using the effective numerical approaches. Some sensitive parameters that are reasonable for disease eliminations are used to obtain the graphical results.