Fractal-Fractional Modeling of the Covid-19 Spread with Deterministic and Stochastic Approaches

It is important to note that the process related to Covid-19 may exhibit random behavior due to environmental noise, and this factor should be taken into account. As a result, the modified Covid-19 model is evaluated using fractal-fractional derivatives in the sense of Caputo–Fabrizio, Caputo, and Atangana–Baleanu within a stochastic framework, aiming to create a more accurate representation of the Covid-19 outbreak. Mathematical analysis, including equilibrium points, the positivity of solutions, and the basic reproduction number for the deterministic model, is included in the study. The existence and uniqueness of solutions for the stochastic model are investigated under certain conditions. Additionally, the conditions for the existence of a global solution of the stochastic model are deduced, and the extinction of the infection within the model is studied. The outcomes of this model, incorporating memory effects, stochastic processes, and fractal properties, are supported by numerical simulations.