Qualitative analysis and numerical simulation of fractal-fractional COVID-19 epidemic model with real data from Pakistan

Abstract

The dynamic of the fractal-fractional COVID-19 epidemic model is studied in this article. The future dynamics of the system are tested by taking the fractal-fractional derivative, which is very effective in formulating the real-life situation by their beneficial memory response. The qualitative analysis of solutions of the proposed COVID-19 model having fractal-fractional derivative has been derived. Also the approximate solution scheme for the considered Fractional-Fractal model has also established. The novel operator of fractal-fractional derivative can be applied to formulate several other dynamics in the real life of complex dimensions in the framework of scientific criteria, too. The threshold number is calculated by utilizing the next-generation matrix approach. The values of the parameters are estimated with the help of least square curve fitting tools. The considered fractal-fractional system was analyzed for theoretical investigation, comprising the uniqueness and existence theory along with Ulam Hyers stability. Sensitivity analysis has been done to examine the most reactive parameters with the basic reproduction number. The fractional Adams-Bashforth AB method has been taken into consideration for the numerical solution.