ABSTRACT
In this work, we modified a dynamical system that addresses COVID-19 infection under a fractal-fractional-order derivative. The model investigates the psychological effects of the disease on humans. We establish global and local stability results for the model under the aforementioned derivative. Additionally, we compute the fundamental reproduction number, which helps predict the transmission of the disease in the community. Using the Carlos Castillo-Chavez method, we derive some adequate results about the bifurcation analysis of the proposed model. We also investigate sensitivity analysis to the given model using the criteria of Chitnis and his co-authors. Furthermore, we formulate the characterization of optimal control strategies by utilizing Pontryagin's maximum principle. We simulate the model for different fractal-fractional orders subject to various parameter values using Adam Bashforth's numerical method. All numerical findings are presented graphically. © 2023 by the authors.
ABSTRACT
In this article, we investigate the dynamics of COVID-19 with a new approach of piecewise global derivative in the sense of singular and non-singular kernels. The singular kernel operator is a Caputo derivative, whereas the non-singular operator is an Atangana-Baleanu Caputo operator. The said problem is investigated for the existence and uniqueness of a solution with a piecewise derivative. The approximate solution to the proposed problem has been obtained by the piecewise numerical iterative technique of Newton polynomials. The numerical scheme for piecewise derivatives in the sense of singular and non-singular kernels is also developed. The numerical simulation for the considered piecewise derivable problem has been drawn up against the available data for different fractional orders. This will be useful for easy understanding of the concept of piecewise global derivatives and the crossover problem dynamics.
ABSTRACT
This work is devoted to studying the transmission dynamics of CoV-2 under the effect of vaccination. The aforesaid model is considered under fractional derivative with variable order of nonsingular kernel type known as Atangan-Baleanue-Caputo (ABC). Fundamental properties of the proposed model including equilibrium points and R0 are obtained by using nonlinear analysis. The existence and uniqueness of solution to the considered model are investigated via fixed point theorems due to Banach and Krasnoselskii. Also, the Ulam-Hyers (UH) approach of stability is used for the said model. Further numerical analysis is investigated by using fundamental theorems of AB fractional calculus and the iterative numerical techniques due to Adams-Bashforth. Numerical simulations are performed by using different values of fractional-variable order ?(??) for the model. The respective results are demonstrated by using real data from Saudi Arabia for graphical presentation.