Mathematical Analysis of Fractal-Fractional Mathematical Model of COVID-19

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.

Keywords

• dynamical system
• fractal-fractional-order derivative
• Pontryagin’s maximum principle
• bifurcation analysis
• sensitivity analysis
• control strategies